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arXiv · 2406.12859

Cohomologies of Reynolds Lie-Yamaguti algebras of any weight and applications

Wen Teng·Shuangjian Guo
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Abstract

The purpose of the present paper is to investigate cohomologies of Reynolds Lie-Yamaguti algebras of any weight and provide some applications. First, we introduce the notion of Reynolds Lie-Yamaguti algebras and give some new examples. Moreover, cohomologies of Reynolds operators and Reynolds Lie-Yamaguti algebras with coefficients in a suitable representation are established. Finally, formal deformations and abelian extensions of Reynolds Lie-Yamaguti algebras are characterized in terms of lower degree cohomology groups.

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Wen Teng, Shuangjian Guo. 2024-03-06. Cohomologies of Reynolds Lie-Yamaguti algebras of any weight and applications. https://arxiv.org/abs/2406.12859

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