Finite-dimensional pointed or copointed Hopf algebras over affine racks

被引：16

作者：

Garcia Iglesias, Agustin ^{[1
,2
]}

Vay, Cristian ^{[1
]}

机构：

[1] Univ Nacl Cordoba, CONICET, FaMAF CIEM, RA-5000 Cordoba, Argentina

[2] Univ Padua, EU, Erasmus Mundus Programme, I-35100 Padua, Italy

来源：

JOURNAL OF ALGEBRA | 2014年 / 397卷

关键词：

Pointed Hopf algebras; Copointed Hopf algebras; Affine racks; Nichols algebras; SPORADIC SIMPLE-GROUPS; NICHOLS ALGEBRAS; SYMMETRIC GROUP; CLASSIFICATION; S-4;

D O I：

10.1016/j.jalgebra.2013.09.009

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the pointed or copointed liftings of Nichols algebras associated to affine racks and constant cocycles for any finite group admitting a principal YD-realization of these racks. In the copointed case we complete the classification for the six affine racks whose Nichols algebra is known to be of finite dimension. In the pointed case our method allows us to finish four of them. In all of the cases the Hopf algebras obtained turn out to be cocycle deformations of their associated graded Hopf algebras. All of them are new examples of finite-dimensional copointed or pointed Hopf algebras over non-abelian groups. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：379 / 406

页数：28

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