Crossed squares of cocommutative Hopf algebras

JOURNAL OF ALGEBRA

卷:584

Article

Sterck, Florence^1,2 

[1] Catholic Univ Louvain, Inst Rech Math & Phys, Chemin Cyclotron 2, B-1348 Louvain La Neuve, Belgium

[2] Univ Libre Bruxelles, Dept Math, Campus Plaine,CP 210 Blvd Triomphe, B-1050 Brussels, Belgium

关键词: Cocommutative Hopf algebras;    Crossed modules;    Crossed squares;    Internal groupoids;    Crossed Lie algebras;   

DOI  :  10.1016/j.jalgebra.2021.05.018

来源: Elsevier

【 摘 要 】

In this paper, we define the notion of Hopf crossed squares for cocommutative Hopf algebras extending the notions of crossed squares of groups and of Lie algebras. We prove the equivalence between the category of Hopf crossed squares and the category of double internal groupoids in the category of cocommutative Hopf algebras. The Hopf crossed squares turn out to be the internal crossed modules in the category of crossed modules in the category of cocommutative Hopf algebras. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free