Article
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Cohomology of Modified Rota-Baxter Pre-lie Algebras and Its Applications
Version 1
: Received: 22 April 2024 / Approved: 22 April 2024 / Online: 23 April 2024 (03:17:05 CEST)
How to cite: Zhu, F.; You, T.; Teng, W. Cohomology of Modified Rota-Baxter Pre-lie Algebras and Its Applications. Preprints 2024, 2024041411. https://doi.org/10.20944/preprints202404.1411.v1 Zhu, F.; You, T.; Teng, W. Cohomology of Modified Rota-Baxter Pre-lie Algebras and Its Applications. Preprints 2024, 2024041411. https://doi.org/10.20944/preprints202404.1411.v1
Abstract
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.
Keywords
Pre-Lie algebras; modified Rota-Baxter operator; cohomology; deformation; abelian extension; pre-Lie 2-algebras
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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