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# Bimodule and twisted representation of vertex operator algebras

Author:
Jiang, QiFen   Jiao, XiangYu

Journal:
Science China Mathematics

Issue Date:
2016

Abstract(summary):

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 $$n \in \tfrac{1} {T}\mathbb{Z}_ +$$, we construct an A g,n (V)-bimodule A g,n (M) and study its properties, discuss the connections between bimodule A g,n (M) and intertwining operators. Especially, bimodule $$A_{g,n - \tfrac{1} {T}} (M)$$ (M) is a natural quotient of 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 $$Hom_{A_{g,n} (V)} \left( {A_{g,n} \left( M \right) \otimes _{A_{g,n} (V)} M^j \left( s \right),M^k \left( t \right)} \right)$$ for s, tn, M j , M k are g-twisted V modules, if V is g-rational.

Page:
397-410

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