Integrals for Finite Tensor Categories

研究成果査読

8 被引用数 (Scopus)

抄録

We introduce the notions of categorical integrals and categorical cointegrals of a finite tensor category C by using a certain adjunction between C and its Drinfeld center Z(C). These notions can be identified with integrals and cointegrals of a finite-dimensional Hopf algebra H if C is the representation category of H. We generalize basic results on integrals and cointegrals of a finite-dimensional Hopf algebra (such as the existence, the uniqueness, and the Maschke theorem) to finite tensor categories. Motivated by results of Lorenz, we also investigate relations between categorical integrals and morphisms factoring through projective objects. Finally, we extend the n-th indicator of a finite-dimensional Hopf algebra introduced by Kashina, Montgomery and Ng to finite tensor categories.

本文言語English
ページ(範囲)459-493
ページ数35
ジャーナルAlgebras and Representation Theory
22
2
DOI
出版ステータスPublished - 2019 4 15

ASJC Scopus subject areas

  • 数学 (全般)

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