Cohomology of Modified Rota-Baxter Pre-lie Algebras and Its Applications

Fuyang Zhu; Taijie You; Wen Teng

doi:10.20944/preprints202404.1411.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 22 April 2024 / Approved: 22 April 2024 / Online: 23 April 2024 (03:17:05 CEST)

Semenov-Tian-Shansky has introduced the modified classical Yang-Baxter equation, which is called the modified $r$-matrix. Relevant studies have been extensive in recent times. This paper is devoted to study cohomology theory of modified Rota-Baxter pre-Lie algebras and its applications. First we introduce the concept and representations of modified Rota-Baxter pre-Lie algebras. We then develop the cohomology of modified Rota-Baxter pre-Lie algebras with coefficients in a suitable representation. As applications, we consider the infinitesimal deformations, abelian extensions and skeletal modified Rota-Baxter pre-Lie 2-algebra in terms of lower degree cohomology groups.

Pre-Lie algebras; modified Rota-Baxter operator; cohomology; deformation; abelian extension; pre-Lie 2-algebras

Computer Science and Mathematics, Algebra and Number Theory

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Cohomology of Modified Rota-Baxter Pre-lie Algebras and Its Applications

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