A note on split extensions of bialgebras-Reference-Cited by-同舟云学术

A note on split extensions of bialgebras

Published:2018-09-01 Issue:5 Volume:30 Page:1089-1095
ISSN:1435-5337
Container-title:Forum Mathematicum
language:
Short-container-title:

Author:

García-Martínez Xabier¹,Van der Linden Tim²

Affiliation:

1. Department of Mathematics, University of Santiago de Compostela, 15782Santiago de Compostela, Spain

2. Institut de Recherche en Mathématique et Physique, Université catholique de Louvain, chemin du cyclotron 2 bte L7.01.02, 1348Louvain-la-Neuve, Belgium

Abstract

AbstractWe prove a universal characterization of Hopf algebras among cocommutative bialgebras over an algebraically closed field: a cocommutative bialgebra is a Hopf algebra precisely when every split extension over it admits a join decomposition. We also explain why this result cannot be extended to a non-cocommutative setting.

Funder

Xunta de Galicia

Ministerio de Economía y Competitividad

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/forum-2017-0016/pdf

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