Systematic VOA catalog
The online database of Vertex Operator Algebras and Tensor Categroies (Version 0.5)
Terry Gannon, Gerald Höhn, Hiroshi Yamauchi, ...
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Table of content
- N=0 Minimal model of central charge: 1/2, 7/10, 4/5,
6/7, 25/28, 11/12, 14/15, 52/55,
21/22, 25/26, 88/91, 34/35, 39/40,
133/136, 50/51, 56/57, 187/190, 69/70,
76/77, 250/253, 91/92, 99/100, 322/325,
116/117, 125/126, 403/406,
144/145, 154/155, ...
- Z_2 extensions of N=0 minimal models of central charge: 4/5, 6/7,
14/15, 52/55,
88/91, 34/35,
50/51, 56/57,
76/77, 250/253,
322/325,116/117,
144/145, 154/155, ...
- Exceptional extensions of N=0 minimal models of central charge: 21/22, 25/26,
144/145, 154/155
- N=1 Minimal models of central charge: 7/10, 1, 81/70,
5/4, 55/42, 27/20, 91/66, 7/5,
405/286, 10/7, 187/230, 81/56, 247/170,
35/34, 945/646, 22/15, 391/266, 81/55,
475/322, 65/44, 1701/1150, 77/52, 667/450,
135/91, 775/522, ...
- N=2 Minimal models of central charge: 1, 3/2, 9/5,
2, 15/7, 9/4, 7/3,
12/5, 27/11, 5/2, 33/13,
18/7, 13/5,
21/8, 45/17,
- VOA for lattice L=Sqrt(2n)Z with n= 1, 2, 3, 4,
5, 6, 7, 8,
9, 10, 11, 12,
13, 14, 15, 16,
17, 18, 19, 20,
21, 22, 23, 24, ...
- Z2-orbifold VOA for lattice L=Sqrt(2n)Z with n=1, 2, 3, 4,
5, 6, 7, 8,
9, 10, 11, 12,
13, 14, 15, 16,
17, 18, 19, 20,
21, 22, 23, 24,
25, 26, ...
- G-orbifold VOA for lattice L=Sqrt(2)Z with G= tetrahedral group, octahedral group, icosahedral group
- Monster dihedral VOAs (affine E8): U1A, U2A, U3A, U4A, U5A,
U6A, U2B, U4B, U3C
- Baby Monster dihedral VOAs (affine E7): UB1A, UB2B, UB3A, UB4B, UB2C and the algebras
VB1A, VB2B, VB3A, VB4B, VB2C
- Fischer group dihedral VOAs (affine E6): UF1A, UF2A, UF3A and the algebras
VF1A, UF2A, VF3A
Based on the Sloane-Nebe catalogue of lattices
- Dimension 1: lat-A1
- Dimension 2: lat-A2, lat-A2*, lat-BGF.2.2112, lat-BGF.2.214, lat-BGF.2.216, lat-BGF.2.414, lat-BGF.2.416, lat-D2
- Dimension 3: lat-A3, lat-cubic F (classical holotype), lat-cubic F (even holotype), lat-cubic I (even holotype), lat-cubic P (even holotype), lat-D3, lat-digonal C (even holotype), lat-digonal F (even holotype), lat-digonal I (even holotype), lat-digonal P (even holotype), lat-hexagonal P (even holotype), lat-monoclinic C (even holotype), lat-monoclinic P (even holotype), lat-tetragonal I (even holotype), lat-tetragonal P (even holotype), lat-triclinic P (even holotype), lat-trigonal R (even holotype), lat-zcc
- Dimension 4: lat-A4, lat-A4*, lat-D4, lat-D4 as a Hurwitzian lattice, lat-E(14), lat-E(15), lat-Elkies_A, lat-Elkies_B, lat-Elkies_C, lat-F4, lat-QQF.4.a, lat-QQF.4.b, lat-QQF.4.f, lat-QQF.4.g, lat-QQF.4.i
- Dimension 5: lat-A5, lat-A5^{+3}, lat-D5
- Dimension 6: lat-6QF.6.b, lat-6QF.6.d, lat-A6, lat-A6*, lat-A6,1, lat-A6^(2), lat-A6,2, lat-D6, lat-E6, lat-E6*
- Dimension 7: lat-A7, lat-D7, lat-E7, lat-E7a, lat-KAPPA7, lat-P7.1, lat-P7.10, lat-P7.11, lat-P7.12, lat-P7.13, lat-P7.14, lat-P7.15, lat-P7.16, lat-P7.17, lat-P7.18, lat-P7.19, lat-P7.20, lat-P7.21, lat-P7.22, lat-P7.23, lat-P7.24, lat-P7.25, lat-P7.26, lat-P7.27, lat-P7.28, lat-P7.29, lat-P7.3, lat-P7.30, lat-P7.31, lat-P7.32, lat-P7.33, lat-P7.4, lat-P7.5, lat-P7.6, lat-P7.7, lat-P7.8, lat-P7.9
- Dimension 8: lat-8QF.8.a, lat-8QF.8.d, lat-8QF.8.e, lat-A2xA4#, lat-A2 x D4, lat-A8, lat-A8*, lat-D8, lat-E8, lat-E8 (as a Hurwitzian lattice), lat-E8 (coding theory version), lat-KAPPA8, lat-KAPPA8*, lat-KAPPA8.2, lat-M8,3, lat-Q8(1), lat-st15moddim8a, lat-st15moddim8b
- Dimension 9: lat-A9, lat-D9, lat-KAPPA9, lat-KAPPA9.2, lat-LAMBDA9,
- Dimension 10: lat-A10, lat-A10*, lat-A10^(2), lat-A10^(3), lat-(C6 x SU(4,2)):C2, lat-D10, lat-KAPPA10, lat-KAPPA10*, lat-LAMBDA10, lat-Q10,
- Dimension 11: lat-A11, lat-D11, lat-KAPPA11, lat-LAMBDA11, lat-LAMBDA11_MIN,
- Dimension 12: lat-((3+^(1+2):SL(2,3)) x SL(2,3)).C2, lat-A12, lat-A12*, lat-A1^6.sqrt(3)A1^6, lat-A2^3.sqrt(3)A2^3, lat-A2xA6, lat-A2 x A6^(2), lat-A2xM6,2, lat-A3^2.sqrt(3)A3^2, lat-A6.sqrt(3)A6, lat-(C2 x C3.Alt6).(C2 x C2), lat-(C2 x D10 x Alt5):C2, lat-C6.PSU(4,3).(C2 x C2), lat-D12, lat-D6.sqrt(D6), lat-E6.sqrt(3)E6, lat-G2^2.D4.sqrt(3)D4, lat-G2^6, lat-G2.A5.sqrt(3)A5, lat-K12, lat-K12 (The Coxeter-Todd Lattice), lat-LAMBDA12, lat-LAMBDA12_MID, lat-LAMBDA12_MIN, lat-(PSL(2,7) x D8):C2, lat-(SL(2,5) Y SL(2,3)).C2,
- Dimension 13: lat-A13, lat-D13, lat-KAPPA13, lat-LAMBDA13, lat-LAMBDA13_MID, lat-LAMBDA13_MIN,
- Dimension 14: lat-A14, lat-A14*, lat-A2 x E7, lat-C2 x G(2,3), lat-C2 x S7, lat-C2 x S8, lat-D14, lat-KAPPA14.1, lat-KAPPA14.2, lat-LAMBDA14, lat-LAMBDA14.2, lat-LAMBDA14.3, lat-LAMBDA14.4, lat-M14,3, lat-M14,6,
- Dimension 15: lat-A15, lat-D15, lat-KAPPA15.1, lat-KAPPA15.2, lat-LAMBDA15, lat-LAMBDA15.2, lat-LAMBDA15.3, lat-LAMBDA15.4,
- Dimension 16: lat-A16, lat-A16*, lat-A16^(3), lat-A2xH4, lat-A4 x F4, lat-BW16 as a Hurwitzian lattice, lat-BW16 (The Barnes-Wall Lattice), lat-C2.Alt10, lat-(C2.Alt7 Y C2.S3).C2, lat-(C2 x Alt6).(C2 x C2), lat-C2 x S3 x PGL(2,7), lat-C2 x (S5 x S5):C2, lat-D120.C2, lat-D120.C2.b, lat-D120.(C4 x C2), lat-D16, lat-E8 x A2, lat-KAPPA16.1, lat-KAPPA16.2, lat-KAPPA16.3, lat-LAMBDA16, lat-LAMBDA16.2, lat-LAMBDA16.3, lat-LAMBDA16.4, lat-(SL(2,5) Y (D8 Y Q8).Alt5).C2, lat-(SL(2,5) Y ((SL(2,3) x C3).C2)).C2, lat-(((SL(2,5) Y SL(2,5)):C2) x D10):C2, lat-(SL(2,5) Y SL(2,9)):C2, lat-(SL(2,7) Y C2.S3).C2, lat-(SL(2,9) Y SL(2,9)).(C2 x C2), lat-((Sp(4,3) x C3) Y SL(2,3)).C2,
- Dimension 17: lat-A17, lat-D17, lat-KAPPA17.1, lat-KAPPA17.2, lat-LAMBDA17, lat-LAMBDA17.2, lat-LAMBDA17.3, lat-LAMBDA17.4, lat-Q1761, lat-Q1763, lat-Qp1761, lat-Qp1763,
- Dimension 18: lat-A18, lat-A18*, lat-A18^(5), lat-A2xA9, lat-(C2 x 3^(1+4):Sp(4,3)).C2, lat-(C2 x PSL(2,7) x PSL(2,7)).(C2 x C2), lat-D18, lat-KAPPA18, lat-LAMBDA18, lat-LAMBDA18.2, lat-LAMBDA18.3, lat-M18,4,
- Dimension 19: lat-A19, lat-D19, lat-KAPPA19, lat-LAMBDA19,
- Dimension 20: lat-A_11.otimes(3).A_2, lat-A20, lat-A20*, lat-A2 x A10, lat-A4 x A5, lat-C2.M12.C2, lat-C2.M22.C2, lat-C2 x 5^(1+2):GL(2,5), lat-(C2 x PSL(3,4)).(C2 x S3), lat-C2 x S3 x PGL(2,11), lat-C2 x S3 x PGL(2,11)(b), lat-(C2 x SU(4,2)).C2, lat-D20, lat-F4 x A5, lat-KAPPA20, lat-L20, lat-L_20,4, lat-L5(P^5), lat-LAMBDA20, lat-M20,3, lat-(PSL(2,11) x D12).C2, lat-R20, lat-(SL(2,11) Y SL(2,3)).C2, lat-(SU(4,2) x C6).C2, lat-(SU(5,2) x SL(2,3)).C2,
- Dimension 21: lat-A21, lat-C2 x Sp(6,2), lat-D21, lat-KAPPA21, lat-LAMBDA21,
- Dimension 22: lat-A22, lat-A22*, lat-A22^(4), lat-A22^(6), lat-A2 x A11, lat-(C2 x Mc).C2, lat-(C2 x PSU(6,2)).S3, lat-D22, lat-hA22^(2), lat-hA22^(3), lat-LAMBDA 22, lat-overlattice(A2xA11),
- Dimension 23: lat-A23, lat-D23, lat-LAMBDA 23,
- Dimension 24: lat-(4+sqrt(5)) x Leech, lat-A24, lat-A24*, lat-A2 x A12, lat-A4xA6, lat-A4 x E6, lat-(Alt5 x ((C3 x D8).C2)).C2, lat-(C2.J2 Y SL(2,5)):C2, lat-((C2 x C3.Alt6).C2 Y SL(2,3)).C2, lat-(C2 x C3.PGL(2,9) x D10).C2, lat-(C2 x D78).C12, lat-C2 x PSL(2,11):C2, lat-((C2 x PSL(3,3)).C2 x C3).C2, lat-(C2 x PSU(4,2)).C2, lat-C2 x S5 x PGL(2,7), lat-(C3.M10 x D8).C2, lat-(C3.M10 x SL(2,3)).C2, lat-(C3.S6 x D8).C2, lat-C6.Alt7:C2, lat-(C6.PSL(3,4).C2 Y D8).C2, lat-(C6.PSU(4,3).C2 Y SL(2,3)).C2, lat-D24, lat-F4 x A6, lat-F4xE6, lat-hLeech24_3, lat-J24, lat-L_24.2, lat-L6(P^6), lat-LAMBDA24 (The Leech Lattice), lat-LAMBDA24 (The Leech lattice as a Hurwitzian lattice), lat-Leech, lat-N(12A2), lat-N(24A1), lat-N(2A12), lat-N(2A7_2D5), lat-N(2A9_D6), lat-N(2D12), lat-N(3A8), lat-N(3D8), lat-N(3E8), lat-N(4A5_D4), lat-N(4A6), lat-N(4D6), lat-N(4E6), lat-N(6A4), lat-N(6D4), lat-N(8A3), lat-N(A11_D7_E6), lat-N(A15_D9), lat-N(A17_E7), lat-N(A24), lat-N(D10_2E7), lat-N(D16_E8), lat-N(D24), lat-(PSL(2,7) x W(F4)).C2, lat-R24, lat-S3 x (C2 x D10 x Alt5).C2, lat-S3 x ((PSL(2,7) x D8).C2), lat-S3 x (SL(2,5) Y SL(2,3)).C2, lat-(SL(2,13) Y SL(2,3)).C2, lat-((SL(2,3) Y C4).C2 x PSU(3,3)).C2, lat-(SL(2,5) Y (C2 x 3^(1+2)).GL(2,3)).C2, lat-(((SL(2,5) Y SL(2,5)):C2) x Alt5).C2, lat-(((SL(2,5) Y SL(2,5)):C2) x Alt5):C2, lat-(SL(2,7) x PSL(2,7)).C2, lat-SL(2,7) Y (C2.S4), lat-(SL(2,7) Y Q16).C2, lat-(Sp(4,3) x 3^(1+2):SL(2,3)).C2, lat-W(F4) x PGL(2,7), lat-W(F4) x S5,
- Dimension >24: see the list of VOAs by the corresponding central charge.
Based on the Sloane-Nebe catalogue of lattices
- Dimension 1: latorb-A1
- Dimension 2: latorb-A2, latorb-A2*, latorb-BGF.2.2112, latorb-BGF.2.214, latorb-BGF.2.216, latorb-BGF.2.414, latorb-BGF.2.416, latorb-D2
- Dimension 3: latorb-A3, latorb-cubic F (classical holotype), latorb-cubic F (even holotype), latorb-cubic I (even holotype), latorb-cubic P (even holotype), latorb-D3, latorb-digonal C (even holotype), latorb-digonal F (even holotype), latorb-digonal I (even holotype), latorb-digonal P (even holotype), latorb-hexagonal P (even holotype), latorb-monoclinic C (even holotype), latorb-monoclinic P (even holotype), latorb-tetragonal I (even holotype), latorb-tetragonal P (even holotype), latorb-triclinic P (even holotype), latorb-trigonal R (even holotype), latorb-zcc
- Dimension 4: latorb-A4, latorb-A4*, latorb-D4, latorb-D4 as a Hurwitzian lattice, latorb-E(14), latorb-E(15), latorb-Elkies_A, latorb-Elkies_B, latorb-Elkies_C, latorb-F4, latorb-QQF.4.a, latorb-QQF.4.b, latorb-QQF.4.f, latorb-QQF.4.g, latorb-QQF.4.i
- Dimension 5: latorb-A5, latorb-A5^{+3}, latorb-D5
- Dimension 6: latorb-6QF.6.b, latorb-6QF.6.d, latorb-A6, latorb-A6*, latorb-A6,1, latorb-A6^(2), latorb-A6,2, latorb-D6, latorb-E6, latorb-E6*
- Dimension 7: latorb-A7, latorb-D7, latorb-E7, latorb-E7a, latorb-KAPPA7, latorb-P7.1, latorb-P7.10, latorb-P7.11, latorb-P7.12, latorb-P7.13, latorb-P7.14, latorb-P7.15, latorb-P7.16, latorb-P7.17, latorb-P7.18, latorb-P7.19, latorb-P7.20, latorb-P7.21, latorb-P7.22, latorb-P7.23, latorb-P7.24, latorb-P7.25, latorb-P7.26, latorb-P7.27, latorb-P7.28, latorb-P7.29, latorb-P7.3, latorb-P7.30, latorb-P7.31, latorb-P7.32, latorb-P7.33, latorb-P7.4, latorb-P7.5, latorb-P7.6, latorb-P7.7, latorb-P7.8, latorb-P7.9
- Dimension 8: latorb-8QF.8.a, latorb-8QF.8.d, latorb-8QF.8.e, latorb-A2xA4#, latorb-A2 x D4, latorb-A8, latorb-A8*, latorb-D8, latorb-E8, latorb-E8 (as a Hurwitzian lattice), latorb-E8 (coding theory version), latorb-KAPPA8, latorb-KAPPA8*, latorb-KAPPA8.2, latorb-M8,3, latorb-Q8(1), latorb-st15moddim8a, latorb-st15moddim8b
- Dimension 9: latorb-A9, latorb-D9, latorb-KAPPA9, latorb-KAPPA9.2, latorb-LAMBDA9,
- Dimension 10: latorb-A10, latorb-A10*, latorb-A10^(2), latorb-A10^(3), latorb-(C6 x SU(4,2)):C2, latorb-D10, latorb-KAPPA10, latorb-KAPPA10*, latorb-LAMBDA10, latorb-Q10,
- Dimension 11: latorb-A11, latorb-D11, latorb-KAPPA11, latorb-LAMBDA11, latorb-LAMBDA11_MIN,
- Dimension 12: latorb-((3+^(1+2):SL(2,3)) x SL(2,3)).C2, latorb-A12, latorb-A12*, latorb-A1^6.sqrt(3)A1^6, latorb-A2^3.sqrt(3)A2^3, latorb-A2xA6, latorb-A2 x A6^(2), latorb-A2xM6,2, latorb-A3^2.sqrt(3)A3^2, latorb-A6.sqrt(3)A6, latorb-(C2 x C3.Alt6).(C2 x C2), latorb-(C2 x D10 x Alt5):C2, latorb-C6.PSU(4,3).(C2 x C2), latorb-D12, latorb-D6.sqrt(D6), latorb-E6.sqrt(3)E6, latorb-G2^2.D4.sqrt(3)D4, latorb-G2^6, latorb-G2.A5.sqrt(3)A5, latorb-K12, latorb-K12 (The Coxeter-Todd Lattice), latorb-LAMBDA12, latorb-LAMBDA12_MID, latorb-LAMBDA12_MIN, latorb-(PSL(2,7) x D8):C2, latorb-(SL(2,5) Y SL(2,3)).C2,
- Dimension 13: latorb-A13, latorb-D13, latorb-KAPPA13, latorb-LAMBDA13, latorb-LAMBDA13_MID, latorb-LAMBDA13_MIN,
- Dimension 14: latorb-A14, latorb-A14*, latorb-A2 x E7, latorb-C2 x G(2,3), latorb-C2 x S7, latorb-C2 x S8, latorb-D14, latorb-KAPPA14.1, latorb-KAPPA14.2, latorb-LAMBDA14, latorb-LAMBDA14.2, latorb-LAMBDA14.3, latorb-LAMBDA14.4, latorb-M14,3, latorb-M14,6,
- Dimension 15: latorb-A15, latorb-D15, latorb-KAPPA15.1, latorb-KAPPA15.2, latorb-LAMBDA15, latorb-LAMBDA15.2, latorb-LAMBDA15.3, latorb-LAMBDA15.4,
- Dimension 16: latorb-A16, latorb-A16*, latorb-A16^(3), latorb-A2xH4, latorb-A4 x F4, latorb-BW16 as a Hurwitzian lattice, latorb-BW16 (The Barnes-Wall Lattice), latorb-C2.Alt10, latorb-(C2.Alt7 Y C2.S3).C2, latorb-(C2 x Alt6).(C2 x C2), latorb-C2 x S3 x PGL(2,7), latorb-C2 x (S5 x S5):C2, latorb-D120.C2, latorb-D120.C2.b, latorb-D120.(C4 x C2), latorb-D16, latorb-E8 x A2, latorb-KAPPA16.1, latorb-KAPPA16.2, latorb-KAPPA16.3, latorb-LAMBDA16, latorb-LAMBDA16.2, latorb-LAMBDA16.3, latorb-LAMBDA16.4, latorb-(SL(2,5) Y (D8 Y Q8).Alt5).C2, latorb-(SL(2,5) Y ((SL(2,3) x C3).C2)).C2, latorb-(((SL(2,5) Y SL(2,5)):C2) x D10):C2, latorb-(SL(2,5) Y SL(2,9)):C2, latorb-(SL(2,7) Y C2.S3).C2, latorb-(SL(2,9) Y SL(2,9)).(C2 x C2), latorb-((Sp(4,3) x C3) Y SL(2,3)).C2,
- Dimension 17: latorb-A17, latorb-D17, latorb-KAPPA17.1, latorb-KAPPA17.2, latorb-LAMBDA17, latorb-LAMBDA17.2, latorb-LAMBDA17.3, latorb-LAMBDA17.4, latorb-Q1761, latorb-Q1763, latorb-Qp1761, latorb-Qp1763,
- Dimension 18: latorb-A18, latorb-A18*, latorb-A18^(5), latorb-A2xA9, latorb-(C2 x 3^(1+4):Sp(4,3)).C2, latorb-(C2 x PSL(2,7) x PSL(2,7)).(C2 x C2), latorb-D18, latorb-KAPPA18, latorb-LAMBDA18, latorb-LAMBDA18.2, latorb-LAMBDA18.3, latorb-M18,4,
- Dimension 19: latorb-A19, latorb-D19, latorb-KAPPA19, latorb-LAMBDA19,
- Dimension 20: latorb-A_11.otimes(3).A_2, latorb-A20, latorb-A20*, latorb-A2 x A10, latorb-A4 x A5, latorb-C2.M12.C2, latorb-C2.M22.C2, latorb-C2 x 5^(1+2):GL(2,5), latorb-(C2 x PSL(3,4)).(C2 x S3), latorb-C2 x S3 x PGL(2,11), latorb-C2 x S3 x PGL(2,11)(b), latorb-(C2 x SU(4,2)).C2, latorb-D20, latorb-F4 x A5, latorb-KAPPA20, latorb-L20, latorb-L_20,4, latorb-L5(P^5), latorb-LAMBDA20, latorb-M20,3, latorb-(PSL(2,11) x D12).C2, latorb-R20, latorb-(SL(2,11) Y SL(2,3)).C2, latorb-(SU(4,2) x C6).C2, latorb-(SU(5,2) x SL(2,3)).C2,
- Dimension 21: latorb-A21, latorb-C2 x Sp(6,2), latorb-D21, latorb-KAPPA21, latorb-LAMBDA21,
- Dimension 22: latorb-A22, latorb-A22*, latorb-A22^(4), latorb-A22^(6), latorb-A2 x A11, latorb-(C2 x Mc).C2, latorb-(C2 x PSU(6,2)).S3, latorb-D22, latorb-hA22^(2), latorb-hA22^(3), latorb-LAMBDA 22, latorb-overlattice(A2xA11),
- Dimension 23: latorb-A23, latorb-D23, latorb-LAMBDA 23,
- Dimension 24: latorb-(4+sqrt(5)) x Leech, latorb-A24, latorb-A24*, latorb-A2 x A12, latorb-A4xA6, latorb-A4 x E6, latorb-(Alt5 x ((C3 x D8).C2)).C2, latorb-(C2.J2 Y SL(2,5)):C2, latorb-((C2 x C3.Alt6).C2 Y SL(2,3)).C2, latorb-(C2 x C3.PGL(2,9) x D10).C2, latorb-(C2 x D78).C12, latorb-C2 x PSL(2,11):C2, latorb-((C2 x PSL(3,3)).C2 x C3).C2, latorb-(C2 x PSU(4,2)).C2, latorb-C2 x S5 x PGL(2,7), latorb-(C3.M10 x D8).C2, latorb-(C3.M10 x SL(2,3)).C2, latorb-(C3.S6 x D8).C2, latorb-C6.Alt7:C2, latorb-(C6.PSL(3,4).C2 Y D8).C2, latorb-(C6.PSU(4,3).C2 Y SL(2,3)).C2, latorb-D24, latorb-F4 x A6, latorb-F4xE6, latorb-hLeech24_3, latorb-J24, latorb-L_24.2, latorb-L6(P^6), latorb-LAMBDA24 (The Leech Lattice), latorb-LAMBDA24 (The Leech lattice as a Hurwitzian lattice), latorb-Leech, latorb-N(12A2), latorb-N(24A1), latorb-N(2A12), latorb-N(2A7_2D5), latorb-N(2A9_D6), latorb-N(2D12), latorb-N(3A8), latorb-N(3D8), latorb-N(3E8), latorb-N(4A5_D4), latorb-N(4A6), latorb-N(4D6), latorb-N(4E6), latorb-N(6A4), latorb-N(6D4), latorb-N(8A3), latorb-N(A11_D7_E6), latorb-N(A15_D9), latorb-N(A17_E7), latorb-N(A24), latorb-N(D10_2E7), latorb-N(D16_E8), latorb-N(D24), latorb-(PSL(2,7) x W(F4)).C2, latorb-R24, latorb-S3 x (C2 x D10 x Alt5).C2, latorb-S3 x ((PSL(2,7) x D8).C2), latorb-S3 x (SL(2,5) Y SL(2,3)).C2, latorb-(SL(2,13) Y SL(2,3)).C2, latorb-((SL(2,3) Y C4).C2 x PSU(3,3)).C2, latorb-(SL(2,5) Y (C2 x 3^(1+2)).GL(2,3)).C2, latorb-(((SL(2,5) Y SL(2,5)):C2) x Alt5).C2, latorb-(((SL(2,5) Y SL(2,5)):C2) x Alt5):C2, latorb-(SL(2,7) x PSL(2,7)).C2, latorb-SL(2,7) Y (C2.S4), latorb-(SL(2,7) Y Q16).C2, latorb-(Sp(4,3) x 3^(1+2):SL(2,3)).C2, latorb-W(F4) x PGL(2,7), latorb-W(F4) x S5,
- Dimension >24: see the list of VOAs by the corresponding central charge.
Type A
- Level 1: A1, A2, A3, A4, A5,
A6, A7, A8, A9, A10,
A11, A12, A13, A14, A15,
A16, A17, A18, A19, A20,
A21, A22, A23, A24, ...
- Level 2: A1, A2, A3, A4, A5,
A6, A7, A8, A9, A10,
A11, A12, A13, A14, A15,
A16, A17, A18, A19, A20,
A21, A22, A23, A24, ...
- Level 3: A1, A2, A3, A4, A5,
A6, A7, A8, A9, A10,
A11, A12, A13, A14, A15,
A16, A17, A1, A1, A1,
A21, A22, A23, A24, ...
- Level 4: A1, A2, A3, A4, A5,
A6, A7, A8, A9, A10,
A11, A12, A13, A14, A15,
A16, A17, A1, A1, A1,
A21, A22, A23, A24, ...
- Level 5: A1, A2, A3, A4, A5,
A6, A7, A8, A9, A10,
A11, A12, A13, A14, A15,
A16, A17, A1, A1, A1,
A21, A22, A23, A24, ...
- Level 6: A1, A2, A3, A4, A5,
A6, A7, A8, A9, A10,
A11, A12, A13, A14, A15,
A16, A17, A1, A1, A1,
A21, A22, A23, A24, ...
- Level 7: A1, A2, A3, A4, A5,
A6, A7, A8, A9, A10,
A11, A12, A13, A14, A15,
A16, A17, A1, A1, A1,
A21, A22, A23, A24, ...
- Level 8: A1, A2, A3, A4, A5,
A6, A7, A8, A9, A10,
A11, A12, A13, A14, A15,
A16, A17, A1, A1, A1,
A21, A22, A23, A24, ...
- Level 9: A1, A2, A3, A4, A5,
A6, A7, A8, A9, A10,
A11, A12, A13, A14, A15,
A16, A17, A1, A1, A1,
A21, A22, A23, A24, ...
- Level 10: A1, A2, A3, A4, A5,
A6, A7, A8, A9, A10,
A11, A12, A13, A14, A15,
A16, A17, A1, A1, A1,
A21, A22, A23, A24, ...
Type B
- Level 1: B1, B2, B3, B4, B5,
B6, B7, B8, B9, B10,
B11, B12, B13, B14, B15,
B16, B17, B1, B1, B1,
B21, B22, B23, B24, ...
- Level 2: B1, B2, B3, B4, B5,
B6, B7, B8, B9, B10,
B11, B12, B13, B14, B15,
B16, B17, B1, B1, B1,
B21, B22, B23, B24, ...
- Level 3: B1, B2, B3, B4, B5,
B6, B7, B8, B9, B10,
B11, B12, B13, B14, B15,
B16, B17, B1, B1, B1,
B21, B22, B23, B24, ...
- Level 4: B1, B2, B3, B4, B5,
B6, B7, B8, B9, B10,
B11, B12, B13, B14, B15,
B16, B17, B1, B1, B1,
B21, B22, B23, B24, ...
- Level 5: B1, B2, B3, B4, B5,
B6, B7, B8, B9, B10,
B11, B12, B13, B14, B15,
B16, B17, B1, B1, B1,
B21, B22, B23, B24, ...
- Level 6: B1, B2, B3, B4, B5,
B6, B7, B8, B9, B10,
B11, B12, B13, B14, B15,
B16, B17, B1, B1, B1,
B21, B22, B23, B24, ...
- Level 7: B1, B2, B3, B4, B5,
B6, B7, B8, B9, B10,
B11, B12, B13, B14, B15,
B16, B17, B1, B1, B1,
B21, B22, B23, B24, ...
- Level 8: B1, B2, B3, B4, B5,
B6, B7, B8, B9, B10,
B11, B12, B13, B14, B15,
B16, B17, B1, B1, B1,
B21, B22, B23, B24, ...
- Level 9: B1, B2, B3, B4, B5,
B6, B7, B8, B9, B10,
B11, B12, B13, B14, B15,
B16, B17, B1, B1, B1,
B21, B22, B23, B24, ...
- Level 10: B1, B2, B3, B4, B5,
B6, B7, B8, B9, B10,
B11, B12, B13, B14, B15,
B16, B17, B1, B1, B1,
B21, B22, B23, B24, ...
Type C
- Level 1: C1, C2, C3, C4, C5,
C6, C7, C8, C9, C10,
C11, C12, C13, C14, C15,
C16, C17, C1, C1, C1,
C21, C22, C23, C24, ...
- Level 2: C1, C2, C3, C4, C5,
C6, C7, C8, C9, C10,
C11, C12, C13, C14, C15,
C16, C17, C1, C1, C1,
C21, C22, C23, C24, ...
- Level 3: C1, C2, C3, C4, C5,
C6, C7, C8, C9, C10,
C11, C12, C13, C14, C15,
C16, C17, C1, C1, C1,
C21, C22, C23, C24, ...
- Level 4: C1, C2, C3, C4, C5,
C6, C7, C8, C9, C10,
C11, C12, C13, C14, C15,
C16, C17, C1, C1, C1,
C21, C22, C23, C24, ...
- Level 5: C1, C2, C3, C4, C5,
C6, C7, C8, C9, C10,
C11, C12, C13, C14, C15,
C16, C17, C1, C1, C1,
C21, C22, C23, C24, ...
- Level 6: C1, C2, C3, C4, C5,
C6, C7, C8, C9, C10,
C11, C12, C13, C14, C15,
C16, C17, C1, C1, C1,
C21, C22, C23, C24, ...
- Level 7: C1, C2, C3, C4, C5,
C6, C7, C8, C9, C10,
C11, C12, C13, C14, C15,
C16, C17, C1, C1, C1,
C21, C22, C23, C24, ...
- Level 8: C1, C2, C3, C4, C5,
C6, C7, C8, C9, C10,
C11, C12, C13, C14, C15,
C16, C17, C1, C1, C1,
C21, C22, C23, C24, ...
- Level 9: C1, C2, C3, C4, C5,
C6, C7, C8, C9, C10,
C11, C12, C13, C14, C15,
C16, C17, C1, C1, C1,
C21, C22, C23, C24, ...
- Level 10: C1, C2, C3, C4, C5,
C6, C7, C8, C9, C10,
C11, C12, C13, C14, C15,
C16, C17, C1, C1, C1,
C21, C22, C23, C24, ...
Type D
- Level 1: D1, D2, D3, D4, D5,
D6, D7, D8, D9, D10,
D11, D12, D13, D14, D15,
D16, D17, D1, D1, D1,
D21, D22, D23, D24, ...
- Level 2: D1, D2, D3, D4, D5,
D6, D7, D8, D9, D10,
D11, D12, D13, D14, D15,
D16, D17, D1, D1, D1,
D21, D22, D23, D24, ...
- Level 3: D1, D2, D3, D4, D5,
D6, D7, D8, D9, D10,
D11, D12, D13, D14, D15,
D16, D17, D1, D1, D1,
D21, D22, D23, D24, ...
- Level 4: D1, D2, D3, D4, D5,
D6, D7, D8, D9, D10,
D11, D12, D13, D14, D15,
D16, D17, D1, D1, D1,
D21, D22, D23, D24, ...
- Level 5: D1, D2, D3, D4, D5,
D6, D7, D8, D9, D10,
D11, D12, D13, D14, D15,
D16, D17, D1, D1, D1,
D21, D22, D23, D24, ...
- Level 6: D1, D2, D3, D4, D5,
D6, D7, D8, D9, D10,
D11, D12, D13, D14, D15,
D16, D17, D1, D1, D1,
D21, D22, D23, D24, ...
- Level 7: D1, D2, D3, D4, D5,
D6, D7, D8, D9, D10,
D11, D12, D13, D14, D15,
D16, D17, D1, D1, D1,
D21, D22, D23, D24, ...
- Level 8: D1, D2, D3, D4, D5,
D6, D7, D8, D9, D10,
D11, D12, D13, D14, D15,
D16, D17, D1, D1, D1,
D21, D22, D23, D24, ...
- Level 9: D1, D2, D3, D4, D5,
D6, D7, D8, D9, D10,
D11, D12, D13, D14, D15,
D16, D17, D1, D1, D1,
D21, D22, D23, D24, ...
- Level 10: D1, D2, D3, D4, D5,
D6, D7, D8, D9, D10,
D11, D12, D13, D14, D15,
D16, D17, D1, D1, D1,
D21, D22, D23, D24, ...
Exceptional types
- E6 level 1, 2, 3, 4
- E7 level 1, 2, 3, 4
- E8 level 1, 2, 3, 4
- F4 level 1, 2, 3, 4
- G2 level 1, 2, 3, 4
- affine Kac Moody VOA A1 level 1: G=Z_1, Z_2, Z_3, Z_5, Z_6, Z_7, Z_8, Z_9, Z_10, D_2, D_3, D_4, D_5, D_6, D_7, D_8, D_9, D_10, T, O, I
- Moonshine module: G=Monster
- central charge 8: S(E8_1)
- central charge 16: S(E8_1^2), S(D16_1)
- central charge 24: V^#, S(C4_10), 69 others
- central charge 32: Z_2 orbifold of rank 32 Barnes Wall lattice VOA, ...
- central charge 40: Z_2 orbifold of VOA associated to an extremal rank 40 lattice, ...
- central charge 48: Z_2 orbifold of VOA associated to the three known extremal rank 48 lattices, hypothetical extremal VOA of c.c. 48, ...
- central charge 72: hypothetical extremal VOA of c.c. 72, ...
- central charge 96: hypothetical extremal VOA of c.c. 96, ...
- central charge 112: hypothetical extremal VOA of c.c. 112, ...
- ...
- central charge 0: Fake Monster
- central charge 8: Fake Baby Monster
- central charge 12:
- central charge 14:
- central charge 16:
- central charge 18:
- central charge 20:
- central charge 24: Monster (1A), Baby Monster (2A), 2B, 3A, 3B, 3C, 4A, 4B, 4C, 4D, 5A, 5B, 6A,, 6B, 6C, 6D, 6E, 6F, 7A, 7b, ..., 27A, 27B, ..., 119AB
- W(2): see minimal models
- W(2,3) of central charge c=
- W(2,4) of central charge c=
- W(2,5) of central charge c=
- W(2,6) of central charge c=
- W(2,7) of central charge c=
- W(2,3,4) of central charge c=
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