Deformations of relative Rota-Baxter operators on Leibniz Triple Systems
Xueru Wu, Yao Ma, Liangyun Chen
TL;DR
This paper develops a cohomology framework for analyzing deformations of relative Rota-Baxter operators on Leibniz triple systems, linking algebraic structures and their deformations.
Contribution
It introduces a cohomology theory for these operators and characterizes their formal deformations and extendibility using this framework.
Findings
Cohomology theory for relative Rota-Baxter operators on Leibniz triple systems
Characterization of formal deformations and their extendibility
Relationship between cohomology of Leibniz algebras and Leibniz triple systems
Abstract
In this paper, we introduce the cohomology theory of relative Rota-Baxter operators on Leibniz triple systems. We use the cohomological approach to study linear and formal deformations of relative Rota-Baxter operators. In particular, formal deformations and extendibility of order deformations of a relative Rota-Baxter operators are also characterized in terms of the cohomology theory. We also consider the relationship between cohomology of relative Rota-Baxter operators on Leibniz algebras and associated Leibniz triple systems.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Rings, Modules, and Algebras