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

Author

Listed:
  • Jia Zhao

    (School of Sciences, Nantong University, Nantong 226019, China)

  • Yu Qiao

    (School of Mathematics and Statistics, Shaanxi Normal University, Xi’an 710119, China)

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.

Suggested Citation

  • Jia Zhao & Yu Qiao, 2024. "Cohomology and Deformations of Relative Rota–Baxter Operators on Lie-Yamaguti Algebras," Mathematics, MDPI, vol. 12(1), pages 1-20, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:1:p:166-:d:1313406
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