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Higher Frobenius-Schur Indicators for Pivotal Categories

Siu-Hung Ng·Peter Schauenburg
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Abstract

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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BibTeXRIS

Siu-Hung Ng, Peter Schauenburg. 2005-12-31. Higher Frobenius-Schur Indicators for Pivotal Categories. https://doi.org/10.1090/conm%2F441%2F08500

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