Finite dimensional Frobenius–Perron algebras
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Published:2024-05-11
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Volume:
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ISSN:0219-4988
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Container-title:Journal of Algebra and Its Applications
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language:en
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Short-container-title:J. Algebra Appl.
Author:
Xu Yongjun1ORCID,
Liu Yikun1ORCID
Affiliation:
1. School of Mathematical Sciences, Qufu Normal University, Qufu 273165, P. R. China
Abstract
Motivated by the Frobenius–Perron (FP) theory of endofunctors of a [Formula: see text]-linear category, we introduce the notion of a FP algebra. This notion can be seen as a generalization of a fusion algebra, and is related to the PP theory of endofunctors of the categories of finite dimensional representations of Taft algebras. Our main result is to classify such algebras with small dimensions according to their FP dimension vectors. Moreover, we introduce the notion of a FP Hopf algebra which can be used to categorify a FP algebra via the Green ring of the Hopf algebra.
Funder
National Natural Science Foundation of China
China Postdoctoral Science Foundation
Undergraduate Teaching Reform Research Project of Shandong Province
Natural Science Foundation of Qufu Normal University
Publisher
World Scientific Pub Co Pte Ltd