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

Fuyang Zhu and Wen Teng ()
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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

Mathematics, 2024, vol. 12, issue 14, 1-17

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.

Keywords: pre-Lie algebra; modified Rota–Baxter operator; cohomology; deformation; abelian extension; pre-Lie 2-algebra; crossed module (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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