## Bibhash Mondal ; Ripan Saha - Cohomology, deformations and extensions of Rota-Baxter Leibniz algebras

cm:10295 - Communications in Mathematics, January 24, 2023, Volume 30 (2022), Issue 2 (Special Issue: CIMPA School "Nonassociative Algebras and Its Applications", Madagascar 2021) - https://doi.org/10.46298/cm.10295
Cohomology, deformations and extensions of Rota-Baxter Leibniz algebras

Authors: Bibhash Mondal ; Ripan Saha

A Rota-Baxter Leibniz algebra is a Leibniz algebra $(\mathfrak{g},[~,~]_{\mathfrak{g}})$ equipped with a Rota-Baxter operator $T : \mathfrak{g} \rightarrow \mathfrak{g}$. 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.

Volume: Volume 30 (2022), Issue 2 (Special Issue: CIMPA School "Nonassociative Algebras and Its Applications", Madagascar 2021)
Published on: January 24, 2023
Accepted on: January 19, 2023
Submitted on: November 11, 2022
Keywords: Mathematics - Rings and Algebras,Mathematics - Representation Theory