Representations of vertex operator superalgebras over an arbitrary field

2022/08/05 by Chongying Dong, Wei Wang · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Nonlinear Waves and Solitons

paper · doi:10.1016/j.jalgebra.2022.07.035

Abstract

An associative algebra A(V) for a vertex operator superalgebra V over an arbitrary algebraically closed field F with chF≠2 is constructed so that the top level of an admissible V-module is naturally an A(V)-module. The highest weight module theory of V is investigated by using A(V) and a one to one correspondence between irreducible A(V)-modules and irreducible admissible V-modules is obtained. Moreover, A(V) is semisimple if V is rational. An A(V)-bimodule A(M) for any admissible V-module M is also constructed and is used to study the fusion rules among V-modules.

Citations

• Local systems of vertex operators, vertex superalgebras and modules
• Integral forms in vertex operator algebras which are invariant under finite groups
• Lattice vertex algebras over fields of prime characteristic

Cited by

• Lattice vertex superalgebras and their modules over fields of prime characteristic

Related

• Vertex Operator Superalgebras and Their Representations
• Twisted representations of vertex operator superalgebras
• Representations of vertex operator algebras
• Modular A_n(V) theory
• Representations of vertex operator algebras and bimodules