Generalized Reynolds Operators on Lie-Yamaguti Algebras

Author:

Teng Wen1,Jin Jiulin2,Long Fengshan1

Affiliation:

1. School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China

2. School of Science, Guiyang University, Guiyang 550005, China

Abstract

In this paper, the notion of generalized Reynolds operators on Lie-Yamaguti algebras is introduced, and the cohomology of a generalized Reynolds operator is established. The formal deformations of a generalized Reynolds operator are studied using the first cohomology group. Then, we show that a Nijenhuis operator on a Lie-Yamaguti algebra gives rise to a representation of the deformed Lie-Yamaguti algebra and a 2-cocycle. Consequently, the identity map will be a generalized Reynolds operator on the deformed Lie-Yamaguti algebra. We also introduce the notion of a Reynolds operator on a Lie-Yamaguti algebra, which can serve as a special case of generalized Reynolds operators on Lie-Yamaguti algebras.

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

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