Cohomologies of Reynolds Lie-Yamaguti algebras of any weight and applications
Wen Teng, Shuangjian Guo
TL;DR
This paper develops a cohomology theory for Reynolds Lie-Yamaguti algebras of any weight, introduces new examples, and explores their deformations and extensions using cohomological methods.
Contribution
It introduces Reynolds Lie-Yamaguti algebras, establishes their cohomologies with coefficients, and characterizes deformations and extensions via cohomology groups.
Findings
Cohomology groups classify formal deformations.
New examples of Reynolds Lie-Yamaguti algebras are provided.
Cohomological criteria for abelian extensions are established.
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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Taxonomy
TopicsAdvanced Topics in Algebra · Nonlinear Waves and Solitons · Algebraic structures and combinatorial models