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.

25 Pages

References in corpus (4)

• Deformations of relative Rota-Baxter operators on Leibniz algebras
• Representations and cohomologies of relative Rota-Baxter Lie algebras and applications
• Cohomology theory of Rota-Baxter pre-Lie algebras of arbitrary weights
• Non-abelian extensions of Rota-Baxter Lie algebras and inducibility of automorphisms

Cited by in corpus (1)

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