
Journal of Lie Theory 33 (2023), No. 2, 641662 Copyright Heldermann Verlag 2023 Representations and Cohomologies of Differential LieYamaguti 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 LieYamaguti algebras with any weights. We introduce the notion of a differential LieYamaguti algebra and its representation. We also consider matched pairs and Manin triples of LieYamaguti algebras. Furthermore, we discuss cohomology theory of a differential LieYamaguti algebra. The deformations and abelian extensions of differential LieYamaguti algebras are also investigated. Keywords: Differential LieYamaguti algebra, representation, matched pair, Manin triple, cohomology, deformation. MSC: 17B99,17A30,16S80. [ Fulltextpdf (157 KB)] for subscribers only. 