Article ID Journal Published Year Pages File Type
4584446 Journal of Algebra 2015 46 Pages PDF
Abstract

In this paper, we introduce the notion of the pivotal cover CpivCpiv of a left rigid monoidal category CC to develop a theoretical foundation for the theory of Frobenius–Schur (FS) indicators in “non-pivotal” settings. For an object V∈CpivV∈Cpiv, the (n,r)(n,r)-th FS indicator νn,r(V)νn,r(V) is defined by generalizing that of an object of a pivotal monoidal category. This notion gives a categorical viewpoint to some recent results on generalizations of FS indicators.Based on our framework, we also study the FS indicators of the “adjoint object” in a finite tensor category, which can be considered as a generalization of the adjoint representation of a Hopf algebra. The indicators of this object closely relate to the space of endomorphisms of the iterated tensor product functor.

Keywords
Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
Authors
,