Structure and cohomology of 3-Lie-Rinehart superalgebras
Abdelkader Ben Hassine, Taoufik Chtioui, Sami Mabrouk, Sergei, Silvestrov
TL;DR
This paper introduces 3-Lie-Rinehart superalgebras, develops their cohomology theory, and explores their relationships with Lie-Rinehart superalgebras, including deformation analysis.
Contribution
It systematically defines 3-Lie-Rinehart superalgebras, constructs their cohomology complex, and investigates their connections and deformations relative to Lie-Rinehart superalgebras.
Findings
Defined 3-Lie-Rinehart superalgebras and their cohomology complex
Established relationships between Lie-Rinehart and 3-Lie-Rinehart superalgebras
Analyzed deformations using cohomology theory
Abstract
We introduce the concept of 3-Lie-Rinehart superalgebra and systematically describe a cohomology complex by considering coefficient modules. Furthermore, we study the relationships between a Lie-Rinehart superalgebra and its induced 3-Lie-Rinehart superalgebra. The deformations of 3-Lie-Rinehart superalgebra are considered via the cohomology theory.
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