The relative modular object and Frobenius extensions of finite Hopf algebras

JOURNAL OF ALGEBRA

卷:471

Article

Shimizu, Kenichi¹ 

[1] Shibaura Inst Technol, Dept Math Sci, Minuma Ku, 307 Fukasaku, Saitama, Saitama 3378570, Japan

关键词: Hopf algebras;    Frobenius extensions;    Tensor categories;    Frobenius functors;   

DOI  :  10.1016/j.jalgebra.2016.09.017

来源: Elsevier

【 摘 要 】

For a certain kind of tensor functor F : C -> D we define the relative modular object XF is an element of D as the difference between a left adjoint and a right adjoint of F. Our main result claims that, if C and V are finite tensor categories, then XF can be written in terms of a categorical analogue of the modular function on a Hopf algebra. Applying this result to the restriction functor associated to an extension A/B of finite-dimensional Hopf algebras, we recover the result of Fischman, Montgomery and Schneider on the Frobenius type property of A/B. We also apply our results to obtain a braided version and a bosonization version of the result of Fischman et al. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free