Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Total Frobenius-Schur Indicators   We define total Frobenius-Schur indicator for each object in a spherical
fusion category $C$ as a certain canonical sum of its higher indicators. The
total indicators are invariants of spherical fusion categories. If $C$ is the
representation category of a semisimple quasi-Hopf algebra $H$, we prove that
the total indicators are non-negative integers which satisfy a certain
divisibility condition. In addition, if $H$ is a Hopf algebra, then all the
total indicators are positive. Consequently, the positivity of total indicators
is a necessary condition for a quasi-Hopf algebra being gauge equivalent to a
Hopf algebra. Certain twisted quantum doubles of finite groups and some
examples of Tambara-Yamagami categories are discussed for the sufficiency of
this positivity condition.

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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: cs
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: gr-qc