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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2023; 60(2): 303-325

Online first article February 20, 2023      Printed March 1, 2023

https://doi.org/10.4134/JKMS.j210676

Copyright © The Korean Mathematical Society.

Relative Rota-Baxter systems on Leibniz algebras

Apurba Das, Shuangjian Guo

Indian Institute of Technology; Guizhou University of Finance and Economics

Abstract

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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.

Keywords: Relative Rota-Baxter system, Leibniz algebra, cohomology, deformation

MSC numbers: Primary 17A32, 17B38

Supported by: This work was financially supported by the NSF of China (No. 12161013) and the innovative exploration and new academic seedling project of Guizhou University of Finance and Economics (No. 2022XSXMA17).

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