10.46298/cm.10295
https://cm.episciences.org/10295
Mondal, Bibhash
Bibhash
Mondal
Saha, Ripan
Ripan
Saha
Cohomology, deformations and extensions of Rota-Baxter Leibniz algebras
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
episciences.org
Mathematics - Rings and Algebras
Mathematics - Representation Theory
Attribution 4.0 International (CC BY 4.0)
2023-01-19
2023-01-24
2023-01-24
eng
journal article
arXiv:2208.00560
10.48550/arXiv.2208.00560
2336-1298
https://cm.episciences.org/10295/pdf
VoR
application/pdf
Communications in Mathematics
Volume 30 (2022), Issue 2 (Special Issue: CIMPA School "Nonassociative Algebras and Its Applications", Madagascar 2021)
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