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Frobenius-Perron dimensions of integral $\Bbb Z_+$-rings and applications

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arxiv 1812.06556 v1 pith:XJGFD7ET submitted 2018-12-16 math.RA

Pavel Etingof This is my paper · ORCID
classification math.RA
keywords algebrasapplicationsdimensionfrobenius-perronintegralnotionquasi-hopfclassification
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abstract

We introduce the notion of the Frobenius-Perron dimension of an integral $\Bbb Z_+$-ring and give some applications of this notion to classification of finite dimensional quasi-Hopf algebras with a unique nontrivial simple module, and of quasi-Hopf and Hopf algebras of prime dimension $p$.

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  1. On Frobenius-Perron Dimension

    math.AG 2019-09 conditional novelty 6.0 of 10

    The generalized Frobenius-Perron dimension of the polynomial representation ring of U(k), defined as the limit over Verlinde algebra truncations, is exactly the ordinary representation dimension, and the paper proves ...

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