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On the Rosenberg-Zelinsky sequence in abelian monoidal categories

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arxiv 0801.0157 v2 pith:V5JV47CZ submitted 2007-12-30 math.CT hep-thmath.QAmath.RA

Till Barmeier , J"urgen Fuchs , Ingo Runkel , Christoph Schweigert This is my paper
classification math.CThep-thmath.QAmath.RA
keywords groupalgebrabimodulesfrobeniusabeliancategorieshomomorphismmonoidal
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We consider Frobenius algebras and their bimodules in certain abelian monoidal categories. In particular we study the Picard group of the category of bimodules over a Frobenius algebra, i.e. the group of isomorphism classes of invertible bimodules. The Rosenberg-Zelinsky sequence describes a homomorphism from the group of algebra automorphisms to the Picard group, which however is typically not surjective. We investigate under which conditions there exists a Morita equivalent Frobenius algebra for which the corresponding homomorphism is surjective. One motivation for our considerations is the orbifold construction in conformal field theory.

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  1. Generalised Orbifolds and G-equivariantisation

    math.QA 2025-06 accept novelty 6.0 of 10

    Generalised orbifold categories of G-crossed ribbon categories are ribbon equivalent to G-equivariantisations, via an explicit functor.

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