On the Rosenberg-Zelinsky sequence in abelian monoidal categories
Abstract
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.
Cite
@article{arxiv.0801.0157,
title = {On the Rosenberg-Zelinsky sequence in abelian monoidal categories},
author = {Till Barmeier and J"urgen Fuchs and Ingo Runkel and Christoph Schweigert},
journal= {arXiv preprint arXiv:0801.0157},
year = {2009}
}
Comments
34 pages, some figures, v2: minor typos corrected, version to be published in J. reine angew. Math. (Crelle)