Higher Frobenius-Schur indicators for pivotal categories Article Swipe

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Endomorphism Mathematics Monoidal category Functor Closed monoidal category Pure mathematics Symmetric monoidal category Frobenius algebra Enriched category Algebra over a field Algebra representation

Peter Schauenburg ·

YOU? · · 2015 · Open Access · · DOI: https://doi.org/10.14288/1.0044472 · OA: W1868028681

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.