Module categories of simple current extensions of vertex operator algebras

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In this article, we study module categries of simple current extensions of vertex operator algebras. Under certain assumptions, we show that every module for a rational vertex operator algebra be lifted to a twisted module for an extended algebra with an abelian symmetry.
latex 14 pages, version 2: English corrected, version 3: Hypotheis I is proved in Lemma 3.1

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