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Rota–Baxter cosystems and coquasitriangular mixed bialgebras
Henan Normal University, Xinxiang, China.
Université de Haute-Alsace, Mulhouse, France.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)ORCID iD: 0000-0003-4554-6528
2021 (English)In: Journal of Algebra and its Applications, ISSN 0219-4988, E-ISSN 1793-6829, Vol. 20, no 04, article id 2150064Article in journal (Refereed) Published
Abstract [en]

In this paper, we present a dual version of T. Brzezinski's results about Rota-Baxter systems which appeared in [Rota-Baxter systems, dendriform algebras and covariant bialgebras, J. Algebra 460 (2016) 1-25]. Then as a generalization to bialgebras, we introduce the notion of Rota-Baxter bisystem and construct various examples of Rota-Baxter bialgebras and bisystems in dimensions 2, 3 and 4. On the other hand, we introduce a new type of bialgebras (named mixed bialgebras) which consist of an associative algebra and a coassociative coalgebra satisfying the compatible condition determined by two coderivations. We investigate coquasitriangular mixed bialgebras and the particular case of coquasitriangular infinitesimal bialgebras, where we give the double construction. Also, we show in some cases that Rota-Baxter cosystems can be obtained from a coquasitriangular mixed bialgebras.

Place, publisher, year, edition, pages
World Scientific Publishing Co. , 2021. Vol. 20, no 04, article id 2150064
Keywords [en]
Rota–Baxter cosystem, Rota–Baxter bisystem, mixed bialgebra, Yang–Baxter equation, coassociative Yang–Baxter pair, coquasitriangular mixed bialgebra, coquasitriangular infinitesimal bialgebra
National Category
Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-51013DOI: 10.1142/S021949882150064XISI: 000645564100007Scopus ID: 2-s2.0-85082331664OAI: oai:DiVA.org:mdh-51013DiVA, id: diva2:1472499
Funder
EU, FP7, Seventh Framework ProgrammeAvailable from: 2020-10-01 Created: 2020-10-01 Last updated: 2024-08-21Bibliographically approved

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