Cohomology and Deformations of Relative Rota–Baxter Operators on Lie-Yamaguti Algebras

Jia Zhao and Yu Qiao ()
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Jia Zhao: School of Sciences, Nantong University, Nantong 226019, China
Yu Qiao: School of Mathematics and Statistics, Shaanxi Normal University, Xi’an 710119, China

Mathematics, 2024, vol. 12, issue 1, 1-20

Abstract: In this paper, we establish the cohomology of relative Rota–Baxter operators on Lie-Yamaguti algebras via the Yamaguti cohomology. Then, we use this type of cohomology to characterize deformations of relative Rota–Baxter operators on Lie-Yamaguti algebras. We show that if two linear or formal deformations of a relative Rota–Baxter operator are equivalent, then their infinitesimals are in the same cohomology class in the first cohomology group. Moreover, an order n deformation of a relative Rota–Baxter operator can be extended to an order n + 1 deformation if and only if the obstruction class in the second cohomology group is trivial.

Keywords: Lie-Yamaguti algebra; relative Rota–Baxter operator; cohomology; deformation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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