Representations of the fixed point subalgebra of the vertex algebra associated to a non-degenerate even lattice by an automorphism of order 2

2020/05/26 by K. TANABE, Tanabe, Kenichiro
Mathematics · #17B69 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2005.12910

openalex publication_date 2020/05/26 · openalex created_date 2020/06/05 · openalex updated_date 2026/07/28

Abstract

Let V_L be the vertex algebra associated to a non-degenerate even lattice L, θ the automorphism of V_L induced from the -1-isometry of L, and V_L⁺ the fixed point subalgebra of V_L under the action of θ. We show that every weak V_L⁺-module is completely reducible.

Citations

• Local systems of vertex operators, vertex superalgebras and modules

Related

• The irreducible weak modules for the fixed point subalgebra of the vertex algebra associated to a non-degenerate even lattice by an automorphism of order 2
• The irreducible weak modules for the fixed point subalgebra of the vertex algebra associated to a non-degenerate even lattice by an automorphism of order 2 (Part 2)
• Classification of irreducible modules for the vertex operator algebra V_L⁺: General case
• Rationality of the vertex operator algebra V_L⁺ for a positive definite even lattice L
• The rank two lattice type vertex operator algebras V_L⁺ and their automorphism groups