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Cohomology and Crossed Modules of Modified Rota–Baxter Pre-Lie Algebras

Author

Listed:
  • Fuyang Zhu

    (School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China)

  • Wen Teng

    (School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China)

Abstract

The goal of the present paper is to provide a cohomology theory and crossed modules of modified Rota–Baxter pre-Lie algebras. We introduce the notion of a modified Rota–Baxter pre-Lie algebra and its bimodule. We define a cohomology of modified Rota–Baxter pre-Lie algebras with coefficients in a suitable bimodule. Furthermore, we study the infinitesimal deformations and abelian extensions of modified Rota–Baxter pre-Lie algebras and relate them with the second cohomology groups. Finally, we investigate skeletal and strict modified Rota–Baxter pre-Lie 2-algebras. We show that skeletal modified Rota–Baxter pre-Lie 2-algebras can be classified into the third cohomology group, and strict modified Rota–Baxter pre-Lie 2-algebras are equivalent to the crossed modules of modified Rota–Baxter pre-Lie algebras.

Suggested Citation

  • Fuyang Zhu & Wen Teng, 2024. "Cohomology and Crossed Modules of Modified Rota–Baxter Pre-Lie Algebras," Mathematics, MDPI, vol. 12(14), pages 1-17, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:14:p:2260-:d:1438982
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