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:: Volume 6, Issue 3 (Vol. 6, No. 3 2020) ::
Mathematical Researches 2020, 6(3): 0-0 Back to browse issues page
Adjunctions between Hom and Tensor as endofunctors of (bi-) module category of comodule algebras over a quasi-Hopf algebra.
Saeid Bagheri Dr.
Malayer University , bagheri_saeid@yahoo.com
Abstract:   (418 Views)

For a Hopf algebra H over a commutative ring k and a left H-module V, the tensor endofunctors V k - and - kV are left adjoint to some kinds of  Hom-endofunctors of _HM. The units and counits of these adjunctions are formally trivial as in the classical case.The category of (bi-) modules over a quasi-Hopf algebra is monoidal and some generalized versions of  Hom-tensor relations have been stated for these (bi-) module categories. However, the units and counits of adjunctions are not trivial.  For a right comodule algebra A over a quasi-Hopf algebra H, the bimodule category _AM_A need not be monoidal and a tensor endofunctors of this category can not be defined trivially. But the coaction of  H on A induces an action of (bi-) module category of  H on the (bi-) module category of the comodule algebra A. 
In this paper, using the action of the monoidal category _HM_H on the bimodule category _AM_A, we introduce suitable versions of tensor and Hom-endofunctors of _AM_A  and generalize varieties the Hom-tensor adjunctions for (bi-) module categories of comodule algebras over a quasi-Hopf algebra H and in any case, we compute the unit and counit of adjunction explicitely.
Keywords: (quasi-)Hopf algebra, Comodule algebra, Monoidal category, Action of a monoidal category.
     
Type of Study: S | Subject: alg
Received: 2018/06/15 | Accepted: 2019/01/28 | Published: 2020/11/30 | ePublished: 2020/11/30
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Bagheri S. Adjunctions between Hom and Tensor as endofunctors of (bi-) module category of comodule algebras over a quasi-Hopf algebra.. Mathematical Researches. 2020; 6 (3)
URL: http://mmr.khu.ac.ir/article-1-2799-en.html


Volume 6, Issue 3 (Vol. 6, No. 3 2020) Back to browse issues page
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