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Hom-algebras and Hom-coalgebras
Université de Haute Alsace, France.
Lund University. (Matematik/tillämpad matematik)ORCID iD: 0000-0003-4554-6528
2010 (English)In: Journal of Algebra and its Applications, ISSN 0219-4988, Vol. 9, no 4, 553-589 p.Article in journal (Refereed) Published
Abstract [en]

The aim of this paper is to develop the theory of Hom-coalgebras and related structures. After reviewing some key constructions and examples of quasi-deformations of Lie algebras involving twisted derivations and giving rise to the class of quasi-Lie algebras incorporating HomLie algebras, we describe the notion and some properties of Hom-algebras and provide examples. We introduce Hom-coalgebra structures, leading to the notions of Hom-bialgebra and HomHopf algebras, and prove some fundamental properties and give examples. Finally, we define the concept of HomLie admissible Hom-coalgebra and provide their classification based on subgroups of the symmetric group.

Place, publisher, year, edition, pages
2010. Vol. 9, no 4, 553-589 p.
National Category
Natural Sciences Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-22061DOI: 10.1142/S0219498810004117ISI: 000281665700004Scopus ID: 2-s2.0-77953351963OAI: oai:DiVA.org:mdh-22061DiVA: diva2:679241
Available from: 2013-12-14 Created: 2013-10-23 Last updated: 2014-06-17Bibliographically approved

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Publisher's full textScopushttp://dx.doi.org/10.1142/S0219498810004117

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Silvestrov, Sergei
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