BiHom-Associative Algebras, BiHom-Lie Algebras and BiHom-Bialgebras

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dc.contributor.authorGraziani, G.
dc.contributor.authorMakhlouf, A.
dc.contributor.authorMenini, C.
dc.contributor.authorPanaite, F.
dc.date.accessioned2019-02-13T17:49:07Z
dc.date.available2019-02-13T17:49:07Z
dc.date.issued2015
dc.description.abstractA BiHom-associative algebra is a (nonassociative) algebra A endowed with two commuting multiplicative linear maps α,β:A→A such that α(a)(bc)=(ab)β(c), for all a,b,c∈A. This concept arose in the study of algebras in so-called group Hom-categories. In this paper, we introduce as well BiHom-Lie algebras (also by using the categorical approach) and BiHom-bialgebras. We discuss these new structures by presenting some basic properties and constructions (representations, twisted tensor products, smash products etc).uk_UA
dc.description.sponsorshipThis paper was written while Claudia Menini was a member of GNSAGA. Florin Panaite was supported by a grant of the Romanian National Authority for Scientific Research, CNCSUEFISCDI, project number PN-II-ID-PCE-2011-3-0635, contract nr. 253/5.10.2011. Parts of this paper have been written while Florin Panaite was a visiting professor at University of Ferrara in September 2014, supported by INdAM, and a visiting scholar at the Erwin Schrodinger Institute in Vienna in July 2014 in the framework of the “Combinatorics, Geometry and Physics” programme; he would like to thank both these institutions for their warm hospitality. The authors are grateful to the referees for their remarks and questions.uk_UA
dc.identifier.citationBiHom-Associative Algebras, BiHom-Lie Algebras and BiHom-Bialgebras / G. Graziani, A. Makhlouf, C. Menini, F. Panaite // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 32 назв. — англ.uk_UA
dc.identifier.issn1815-0659
dc.identifier.other2010 Mathematics Subject Classification: 17A99; 18D10; 16T99
dc.identifier.otherDOI:10.3842/SIGMA.2015.086
dc.identifier.urihttps://nasplib.isofts.kiev.ua/handle/123456789/147155
dc.language.isoenuk_UA
dc.publisherІнститут математики НАН Україниuk_UA
dc.relation.ispartofSymmetry, Integrability and Geometry: Methods and Applications
dc.statuspublished earlieruk_UA
dc.titleBiHom-Associative Algebras, BiHom-Lie Algebras and BiHom-Bialgebrasuk_UA
dc.typeArticleuk_UA

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Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11, випуск за цей рік