Abstract

We introduce a 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 a cohomology theory.

中文翻译：

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3-Lie-Rinehart 超代数的结构和上同调

摘要

我们引入了 3-Lie-Rinehart 超代数的概念，并通过考虑系数模块系统地描述了一个上同调复形。此外，我们研究了 Lie-Rinehart 超代数与其诱导的 3-Lie-Rinehart 超代数之间的关系。3-Lie-Rinehart 超代数的变形是通过上同调理论考虑的。