Ribbon categories and (unoriented) CFT: Frobenius algebras, automorphisms, reversions

Details Ribbon categories and (unoriented) CFT: Frobenius algebras, automorphisms, reversions Ribbon categories and (unoriented) CFT: Frobenius algebras, automorphisms, reversions

2005-11-23

arxiv.org/abs/math/0511590v1

Contemp.Math.431:203-224,2007

Mathematics

Category Theory

22 pages

Scientific paper

A Morita class of symmetric special Frobenius algebras A in the modular tensor category of a chiral CFT determines a full CFT on oriented world sheets. For unoriented world sheets, A must in addition possess a reversion, i.e. an isomorphism from A^opp to A squaring to the twist. Any two reversions of an algebra A differ by an element of the group Aut(A) of algebra automorphisms of A. We establish a group homomorphism from Aut(A) to the Picard group of the bimodule category C_AA, with kernel consisting of the inner automorphisms, and we refine Morita equivalence to an equivalence relation between algebras with reversion.

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