Twisted bimodules and associative algebras associated to VOAs

2025/12/05 by Xu, Shun
#17B69 #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2512.05605

Abstract

Let V be a vertex operator algebra, g be an automorphism of V of order T, and m, n ∈ (1/T)ℕ. In~\citeHX2 and~\citeHXX1, it was shown respectively that the associative algebra A_g,n(V) constructed by Dong, Li, and Mason~\citeDLM3, and the A_g,n(V) - A_g,m(V)-bimodule A_g,n,m(V) constructed by Dong and Jiang~\citeDJ2, are both isomorphic to certain subquotients of U(V[g]), where U(V[g]) denotes the universal enveloping algebra of V with respect to g. In this paper, we give a unified and concise proof of these isomorphisms.

Citations

• Bimodules and g-rationality of vertex operator algebras
• Bimodules associated to vertex operator algebras
• Differential equations, duality and modular invariance
• Twisted representations of vertex operator algebras and associative algebras
• Vertex operator algebras and associative algebras
• Twisted representations of vertex operator algebras
• Vertex Operator Superalgebras and Their Representations

Related

• Refining twisted bimodules associated to VOAs
• Bimodules and g-rationality of vertex operator algebras
• Twisted representations of vertex operator algebras and associative algebras
• Twisted associative algebras associated to vertex algebras
• Lifts of automorphisms of vertex operator algebras in simple current extensions