Journal of Lie Theory 33 (2023), No. 2, 641--662
Copyright Heldermann Verlag 2023
Representations and Cohomologies of Differential Lie-Yamaguti Algebras with any Weights
Qinxiu Sun
Dept. of Mathematics, Zhejiang University of Science and Technology, Hangzhou, China
qxsun@126.com
Shan Chen
Dept. of Mathematics, Zhejiang University of Science and Technology, Hangzhou, China
1844785776@qq.com
The goal of the present paper is to provide representation and cohomological theory of differential Lie-Yamaguti algebras with any weights. We introduce the notion of a differential Lie-Yamaguti algebra and its representation. We also consider matched pairs and Manin triples of Lie-Yamaguti algebras. Furthermore, we discuss cohomology theory of a differential Lie-Yamaguti algebra. The deformations and abelian extensions of differential Lie-Yamaguti algebras are also investigated.
Keywords: Differential Lie-Yamaguti algebra, representation, matched pair, Manin triple, cohomology, deformation.
MSC: 17B99,17A30,16S80.
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