RELATIVE ROTA-BAXTER SYSTEMS ON LEIBNIZ ALGEBRAS

In this paper, we introduce relative Rota-Baxter systems on Leibniz algebras and give some characterizations and new constructions. Then we construct a graded Lie algebra whose Maurer-Cartan elements are relative Rota-Baxter systems. This allows us to define a cohomology theory associated with a rel...

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Bibliographic Details
Published inJournal of the Korean Mathematical Society Vol. 60; no. 2; pp. 303 - 325
Main Authors Apurba Das, Shuangjian Guo
Format Journal Article
LanguageKorean
Published 2023
Subjects
Relative Rota-Baxter system
cohomology
Leibniz algebra
deformation
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Summary:In this paper, we introduce relative Rota-Baxter systems on Leibniz algebras and give some characterizations and new constructions. Then we construct a graded Lie algebra whose Maurer-Cartan elements are relative Rota-Baxter systems. This allows us to define a cohomology theory associated with a relative Rota-Baxter system. Finally, we study formal deformations and extendibility of finite order deformations of a relative Rota-Baxter system in terms of the cohomology theory.
Bibliography:KISTI1.1003/JNL.JAKO202313043202366
ISSN:0304-9914