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Symmetry, Integrability and Geometry: Methods and Applications, 2015, Volume 11, 086, 34 pp.
DOI: https://doi.org/10.3842/SIGMA.2015.086 (Mi sigma1067) 		 
This article is cited in 60 scientific papers (total in 60 papers)

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

Giacomo Graziania, Abdenacer Makhloufb, Claudia Meninic, Florin Panaited

a Université Joseph Fourier Grenoble I Institut Fourier, 100, Rue des Maths BP74 38402 Saint-Martin-d’Hères, France
b Université de Haute Alsace, Laboratoire de Mathématiques, Informatique et Applications, 4, Rue des frères Lumière, F-68093 Mulhouse, France
c University of Ferrara, Department of Mathematics, Via Machiavelli 30, Ferrara, I-44121, Italy
d Institute of Mathematics of the Romanian Academy, PO-Box 1-764, RO-014700 Bucharest, Romania
Full-text PDF (537 kB) Citations (60)
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DOI: https://doi.org/10.3842/SIGMA.2015.086
Abstract: A BiHom-associative algebra is a (nonassociative) algebra $A$ endowed with two commuting multiplicative linear maps $\alpha , \beta\colon A\rightarrow A$ such that $\alpha (a)(bc)=(ab)\beta (c)$, for all $a, b, c\in A$. 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).
Keywords: BiHom-associative algebra; BiHom-Lie algebra; BiHom-bialgebra; representation; twisting; smash product.
Received: May 12, 2015; in final form October 13, 2015; Published online October 25, 2015
Bibliographic databases:
Document Type: Article
MSC: 17A99; 18D10; 16T99
Language: English
Citation: Giacomo Graziani, Abdenacer Makhlouf, Claudia Menini, Florin Panaite, “BiHom-Associative Algebras, BiHom-Lie Algebras and BiHom-Bialgebras”, SIGMA, 11 (2015), 086, 34 pp.
Citation in format AMSBIB
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\by Giacomo~Graziani, Abdenacer~Makhlouf, Claudia~Menini, Florin~Panaite
\paper BiHom-Associative Algebras, BiHom-Lie Algebras and BiHom-Bialgebras
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\vol 11
\papernumber 086
\totalpages 34
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    • This publication is cited in the following 60 articles:
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    		Symmetry, Integrability and Geometry: Methods and Applications
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