Cohomology, deformations and extensions of Rota-Baxter Leibniz algebras

Abstract

A Rota-Baxter Leibniz algebra is a Leibniz algebra $(\mathfrak{g},[,{]}_{\mathfrak{g}})$ equipped with a Rota-Baxter operator $T:\mathfrak{g}\to \mathfrak{g}$. We define representation and dual representation of Rota-Baxter Leibniz algebras. Next, we define a cohomology theory of Rota-Baxter Leibniz algebras. We also study the infinitesimal and formal deformation theory of Rota-Baxter Leibniz algebras and show that our cohomology is deformation cohomology. Moreover, We define an abelian extension of Rota-Baxter Leibniz algebras and show that equivalence classes of such extensions are related to the cohomology groups.

arXiv comment25 Pages

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Cited by in corpus (1)

• The algebraic and geometric classification of right alternative and semi-alternative algebras