Cohomolgies of Rota-Baxter operators on Lie superalgebras and some classifications on Witt superalgebras

In this paper, we introduce the cohomology of Rota-Baxter operators on Lie superalgebras. We define the cohomology of a Rota-Baxter operator R as the Chevalley Eilenberg cohomology of a certain Lie superalgebra induced by R with coefficients in a suitable representation. Then, we give the classifica...

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Bibliographic Details
Published in:Journal of geometry and physics 2023-03, Vol.185, p.104733, Article 104733
Main Authors: Amor, R., Athmouni, N., Ben Hassine, A., Chtioui, T., Mabrouk, S.
Format: Article
Language:English
Subjects:
Cohomology
Pre-Lie superalgebra
Rota-Baxter operator
Witt superalgebra
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Summary:In this paper, we introduce the cohomology of Rota-Baxter operators on Lie superalgebras. We define the cohomology of a Rota-Baxter operator R as the Chevalley Eilenberg cohomology of a certain Lie superalgebra induced by R with coefficients in a suitable representation. Then, we give the classification of the homogeneous Rota-Baxter operators of weight 0 on the Witt superalgebras. To apply our approach, we construct pre-Lie superalgebras from the homogeneous Rota-Baxter operators of weight 0 and their subadjacent Lie superalgebras.
ISSN:0393-0440
1879-1662
DOI:10.1016/j.geomphys.2022.104733