Z₃ symmetry and W₃ algebra in lattice vertex operator algebras

2003/02/25 by C. Dong, Chongying Dong, C. H. Lam +12
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.QA

paper · pdf · doi:10.48550/arxiv.math/0302314

46 pages, latex

arxiv created 2003/02/25 · openalex publication_date 2003/02/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The W₃ algebra of central charge 6/5 is realized as a subalgebra of the vertex operator algebra V_√(2)A2 associated with a lattice of type √(2)A₂ by using both coset construction and orbifold theory. It is proved that W₃ is rational. Its irreducible modules are classified and constructed explicitly. The characters of those irreducible modules are also computed.

Citations

• Symmetric invariant bilinear forms on vertex operator algebras
• Uniform product of A_g,n(V) for an orbifold model V and G-twisted Zhu algebra

Related

• Representations of the vertex operator algebra V_L₂^A₄
• Application of a ℤ₃-orbifold construction to the lattice vertex operator algebras associated to Niemeier lattices
• A characterization of the rational vertex operator algebra V_\Zα⁺: II
• A construction of admissible A₁⁽¹⁾-modules of level -4/3
• A characterization of vertex operator algebras V_Zα⁺: I