{"docId":10827,"paperId":10295,"url":"https:\/\/cm.episciences.org\/10295","doi":"10.46298\/cm.10295","journalName":"Communications in Mathematics","issn":"1804-1388","eissn":"2336-1298","volume":[{"vid":622,"name":"Volume 30 (2022), Issue 2 (Special Issue: CIMPA School \"Nonassociative Algebras and Its Applications\", Madagascar 2021)"}],"section":[],"repositoryName":"arXiv","repositoryIdentifier":"2208.00560","repositoryVersion":3,"repositoryLink":"https:\/\/arxiv.org\/abs\/2208.00560v3","dateSubmitted":"2022-11-11 15:39:58","dateAccepted":"2023-01-19 08:46:15","datePublished":"2023-01-24 11:12:47","titles":["Cohomology, deformations and extensions of Rota-Baxter Leibniz algebras"],"authors":["Mondal, Bibhash","Saha, Ripan"],"abstracts":["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.","Comment: 25 Pages"],"keywords":["Mathematics - Rings and Algebras","Mathematics - Representation Theory"]}