Symmetry, Integrability and Geometry: Methods and Applications
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


SIGMA:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

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 61 scientific papers (total in 61 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 (61)
References:
PDF
HTML
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
\Bibitem{GraMakMen15}
\by Giacomo~Graziani, Abdenacer~Makhlouf, Claudia~Menini, Florin~Panaite
\paper BiHom-Associative Algebras, BiHom-Lie Algebras and BiHom-Bialgebras
\jour SIGMA
\yr 2015
\vol 11
\papernumber 086
\totalpages 34
\mathnet{http://mi.mathnet.ru/sigma1067}
\crossref{https://doi.org/10.3842/SIGMA.2015.086}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000363685400001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84945314347}
Linking options:
  • https://www.mathnet.ru/eng/sigma1067
  • https://www.mathnet.ru/eng/sigma/v11/p86
    • This publication is cited in the following 61 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Symmetry, Integrability and Geometry: Methods and Applications
    Statistics & downloads:
    Abstract page:255
    Full-text PDF :63
    References:33
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024