Bimodule and twisted representation of vertex operator algebras

Abstract

In this paper, for a vertex operator algebra $V$ with an automorphism $g$ of order $T,$ an admissible $V$-module $M$ and a fixed nonnegative rational number $n\in \frac{1}{T}{\mathbb{Z}}_{+},$ we construct an $A_{g,n}(V)$-bimodule ${\mathring{A}}_{g,n}(M)$ and study its some properties, discuss the connections between bimodule ${\mathring{A}}_{g,n}(M)$ and intertwining operators. Especially, bimodule ${\mathring{A}}_{g,n-\frac{1}{T}}(M)$ is a natural quotient of ${\mathring{A}}_{g,n}(M)$ and there is a linear isomorphism between the space ${\mathcal{I}}_{M{M}^j}^{M^k}$ of intertwining operators and the space of homomorphisms ${\mathrm{Hom}}_{{\mathrm{A}}_{\mathrm{g},\mathrm{n}}(\mathrm{V})}({\mathring{\mathrm{A}}}_{\mathrm{g},\mathrm{n}}(\mathrm{M}){\otimes }_{{\mathrm{A}}_{\mathrm{g},\mathrm{n}}(\mathrm{V})}{\mathrm{M}}^{\mathrm{j}}(\mathrm{s}),{\mathrm{M}}^{\mathrm{k}}(\mathrm{t}))$ for $s,t\le n,M^j,M^k$ are $g$-twisted $V$ modules, if $V$ is $g$-rational.

References in corpus (3)

• Modular invariance of trace functions in orbifold theory
• Simple currents and extensions of vertex operator algebras
• Conformal Field Theories, Representations and Lattice Constructions

Cited by in corpus (2)

• Twisted restricted conformal blocks of vertex operator algebras I: $g$-twisted correlation functions and fusion rules
• Bimodules over twisted Zhu algebras and twisted fusion rules theorem for vertex operator algebras