Generalized Yetter–Drinfeld (quasi)modules and Yetter–Drinfeld–Long bi(quasi)modules for Hopf quasigroups-Reference-Cited by-同舟云学术

Generalized Yetter–Drinfeld (quasi)modules and Yetter–Drinfeld–Long bi(quasi)modules for Hopf quasigroups

Published:2019-02 Issue:02 Volume:18 Page:1950034
ISSN:0219-4988
Container-title:Journal of Algebra and Its Applications
language:en
Short-container-title:J. Algebra Appl.

Author:

Shi Gui-Qi¹,Fang Xiao-Li²,Torrecillas Blas³

Affiliation:

1. College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, P. R. China

2. Department of Mathematics, Shaoxing College of Arts and Sciences, Shaoxing 312000, P. R. China

3. Department of Algebra and Analysis, University of Almeria, Almeria 04071, Spain

Abstract

As generalizations of Yetter–Drinfeld module over a Hopf quasigroup, we introduce the notions of Yetter–Drinfeld–Long bimodule and generalize the Yetter–Drinfeld module over a Hopf quasigroup in this paper, and show that the category of Yetter–Drinfeld–Long bimodules [Formula: see text] over Hopf quasigroups is braided, which generalizes the results in Alonso Álvarez et al. [Projections and Yetter–Drinfeld modules over Hopf (co)quasigroups, J. Algebra 443 (2015) 153–199]. We also prove that the category of [Formula: see text] having all the categories of generalized Yetter–Drinfeld modules [Formula: see text], [Formula: see text] as components is a crossed [Formula: see text]-category.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219498819500348

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