Higher Frobenius-Schur Indicators for Pivotal Categories

Details Higher Frobenius-Schur Indicators for Pivotal Categories Higher Frobenius-Schur Indicators for Pivotal Categories

2005-03-08

arxiv.org/abs/math/0503167v2

Contemporary Mathematics 441 (2007), 63-90 (Final Version)

Mathematics

Quantum Algebra

A paragraph which describes the organization of the paper has been added to the introduction. Some observations have been adde

Scientific paper

We define higher Frobenius-Schur indicators for objects in linear pivotal monoidal categories. We prove that they are category invariants, and take values in the cyclotomic integers. We also define a family of natural endomorphisms of the identity endofunctor on a $k$-linear semisimple rigid monoidal category, which we call the Frobenius-Schur endomorphisms. For a $k$-linear semisimple pivotal monoidal category -- where both notions are defined --, the Frobenius-Schur indicators can be computed as traces of the Frobenius-Schur endomorphisms.

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