3-state Potts model and automorphisms of vertex operator algebras of order 3

zbMath1022.17020arXivq-alg/9710038MaRDI QIDQ5942785

Masahiko Miyamoto

Publication date: 15 April 2003

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/q-alg/9710038

zbMATH Keywords

automorphismfusion rulesGriess algebrasimple vertex operator algebra

Mathematics Subject Classification ID

Vertex operators; vertex operator algebras and related structures (17B69) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (13)

Sigma involutions associated with parafermion vertex operator algebra K(sl2,k) ⋮ Quantum dimensions and fusion rules of the VOA \(V_{L_{\mathcal{C} \times \mathcal{D}}}^\tau\) ⋮ Fixed point subalgebras of lattice vertex operator algebras by an automorphism of order three ⋮ Vertex operator algebras generated by two Ising vectors ⋮ The 3-state Potts model and Rogers-Ramanujan series ⋮ On 3-transposition groups generated by \(\sigma\)-involutions associated to \(c=4/5\) Virasoro vectors ⋮ Vertex operator algebra with two Miyamoto involutions generating \(S_{3}\). ⋮ Vertex operator algebras generated by two conformal vectors whose \(\tau\)-involutions generate \(S_{3}\). ⋮ Decomposition of the lattice vertex operator algebra \(V_{\sqrt{2}A_l}\). ⋮ A class of vertex operator algebras constructed from \(\mathbb{Z}_8\) codes ⋮ A new existence proof of the Monster by VOA theory ⋮ McKay's \(E_6\) observation on the largest Fischer group ⋮ Griess algebras generated by the Griess algebras of two \(3A\)-algebras with a common axis

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• A simple construction for the Fischer-Griess monster group
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• Griess algebras and conformal vectors in vertex operator algebras
• Ternary codes and vertex operator algebras
• Vertex algebras, Kac-Moody algebras, and the Monster
• On axiomatic approaches to vertex operator algebras and modules

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