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In this paper, we prove the categories of lower bounded twisted modules ofpositive integer levels for simple vertex operator algebras associated withaffine Lie algebras and general automorphisms are semisimple, using the twistedgeneralization of Zhu's algebra for these vertex operator algebras, constructedin \cite{HY}. We also show that the category of lower bounded twisted modulesfor a general automorphism is equivalent to the category of lower boundedtwisted modules for the corresponding diagram automorphism.

Twisted representations of vertex operator algebras associated to affine Lie algebras