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Malcev Yang-Baxter equation, weighted O-operators on Malcev algebras and post-Malcev algebras
University of Sfax, Faculty of Sciences Sfax, BP 1171, Sfax, 3038, Tunisia.
University of Gafsa, Faculty of Sciences Gafsa, Gafsa, 2112, Tunisi.
University of Gafsa, Faculty of Sciences Gafsa, Gafsa, 2112, Tunisi.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)ORCID iD: 0000-0003-4554-6528
2023 (English)In: Hacettepe Journal of Mathematics and Statistics, ISSN 2651-477X, Vol. 52, no 5, p. 1151-1171Article in journal (Refereed) Published
Abstract [en]

The purpose of this paper is to study the O-operators on Malcev algebras and discuss the solutions of Malcev Yang-Baxter equation by O-operators. Furthermore we introduce the notion of weighted O-operators on Malcev algebras, which can be characterized by graphs of the semi-direct product Malcev algebra. Then we introduce a new algebraic structure called post-Malcev algebras. Therefore, post-Malcev algebras can be viewed as the underlying algebraic structures of weighted O-operators on Malcev algebras. A post-Malcev algebra also gives rise to a new Malcev algebra. Post-Malcev algebras are analogues for Malcev algebras of post-Lie algebras and fit into a bigger framework with a close relationship with post-alternative algebras. 

Place, publisher, year, edition, pages
Hacettepe University , 2023. Vol. 52, no 5, p. 1151-1171
Keywords [en]
alternative algebra, Malcev algebra, Malcev Yang-Baxter equation, representation, Rota-Baxter operator, weighted O-operator
National Category
Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-64793DOI: 10.15672/hujms.1126978ISI: 001104633800002Scopus ID: 2-s2.0-85176130825OAI: oai:DiVA.org:mdh-64793DiVA, id: diva2:1813816
Available from: 2023-11-22 Created: 2023-11-22 Last updated: 2023-12-27Bibliographically approved

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Silvestrov, Sergei

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