Racks, Leibniz algebras and Yetter--Drinfel'd modules

Kraehmer, U. and Wagemann, F. (2015) Racks, Leibniz algebras and Yetter--Drinfel'd modules. Georgian Mathematical Journal, 22(4), pp. 529-542. (doi: 10.1515/gmj-2015-0049)

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A Hopf algebra object in Loday and Pirashvili's category of linear maps entails an ordinary Hopf algebra and a Yetter–Drinfel'd module. We equip the latter with a structure of a braided Leibniz algebra. This provides a unified framework for examples of racks in the category of coalgebras discussed recently by Carter, Crans, Elhamdadi and Saito.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Kraehmer, Dr Ulrich
Authors: Kraehmer, U., and Wagemann, F.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Georgian Mathematical Journal
Publisher:Walter de Gruyter GmbH
ISSN (Online):1572-9176
Published Online:05 November 2015
Copyright Holders:Copyright © 2015 The Authors
First Published:First published in Georgian Mathematical Journal 22(4):529-542
Publisher Policy:Reproduced under a Creative Commons License
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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
586201Homological algebra in monoidal categories: From Hopf algebroids to operads and back.Ulrich KraehmerEngineering & Physical Sciences Research Council (EPSRC)EP/J012718/1M&S - MATHEMATICS