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Rota–Baxter cosystems and coquasitriangular mixed bialgebras

School of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, P. R. China

T. Ma’s current address: Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, Henan Normal University, China

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Abdenacer Makhlouf

Département de Mathématiques, Université de Haute Alsace, IRIMAS, 6 rue des Frères Lumière F-68093 Mulhouse, France

E-mail Address: abdenacer.makhlouf@uha.fr

Corresponding author.

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Sergei Silvestrov

Division of Applied Mathematics, School of Education, Culture and Communication, Mälardalen University, 72123 Västeräs, Sweden

E-mail Address: sergei.silvestrov@mdh.se

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https://doi.org/10.1142/S021949882150064XCited by:15 (Source: Crossref)

Abstract

In this paper, we present a dual version of T. Brzeziński’s results about Rota–Baxter systems which appeared in [Rota–Baxter systems, dendriform algebras and covariant bialgebras, J. Algebra460 (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.

Communicated by A. Leroy

Keywords:

AMSC: 16T05, 16W99

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