Twisted ϕ-coordinated modules for vertex algebras and Zhu's correspondence theorem

2025/12/01 by Xu, Shun
#17B69 #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2512.01272

Abstract

Let V be a vertex algebra and g be an automorphism of V of order T. For any n, m ∈ (1/T)ℕ, we construct an A_g,n(V) - A_g,m(V)-bimodule A_g,n,m(V), where A_g,n(V) denotes the associative algebra constructed by the authors in \citeShun1. We introduce the notion of (1/T)ℕ-graded g-twisted ϕ-coordinated V-modules and prove that there exists a bijection between the simple A_g(V)-modules and the irreducible (1/T)ℕ-graded g-twisted ϕ-coordinated V-modules, where A_g(V)=A_g,0(V). We construct the universal enveloping algebra U(V[g]), showing that A_g(V) is subquotient of U(V[g]). When V is vertex operator algebra, we show that each A_g,n,m(V) is isomorphic to the A_g,n(V)-A_g,m(V)-bimodule A_g,n,m(V) constructed by Dong and Jiang~\citeDJ2. Also we prove that there exists a bijection between the irreducible admissible g-twisted V-modules and the irreducible (1/T)ℕ-graded g-twisted ϕ-coordinated V-modules.

Citations

• Twisted associative algebras associated to vertex algebras
• Refining twisted bimodules associated to VOAs
• Twisted regular representations and bimodules in vertex operator algebra theory
• Twisted regular representations of vertex operator algebras
• ϕ-coordinated modules for quantum vertex algebras and associative algebras
• Bimodules and g-rationality of vertex operator algebras
• Bimodules associated to vertex operator algebras
• Twisted representations of vertex operator superalgebras
• 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

• Bimodules over twisted Zhu algebras and twisted fusion rules theorem for vertex operator algebras
• Bimodues associated to twisted modules of vertex operator algebras and fusion rules
• Bimodules and g-rationality of vertex operator algebras
• Associative algebras for (logarithmic) twisted modules for a vertex operator algebra
• Twisted bimodules and associative algebras associated to VOAs