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.
1
Dept. of Mathematics, Zhejiang University of Science and Technology, Hangzhou, China
Qinxiu Sun; Shan Chen. Representations and Cohomologies of Differential Lie-Yamaguti Algebras with any Weights. Journal of Lie Theory, Tome 33 (2023) no. 2, pp. 641-662. http://geodesic.mathdoc.fr/item/JOLT_2023_33_2_a7/
@article{JOLT_2023_33_2_a7,
author = {Qinxiu Sun and Shan Chen},
title = {Representations and {Cohomologies} of {Differential} {Lie-Yamaguti} {Algebras} with any {Weights}},
journal = {Journal of Lie Theory},
pages = {641--662},
year = {2023},
volume = {33},
number = {2},
url = {http://geodesic.mathdoc.fr/item/JOLT_2023_33_2_a7/}
}
TY - JOUR
AU - Qinxiu Sun
AU - Shan Chen
TI - Representations and Cohomologies of Differential Lie-Yamaguti Algebras with any Weights
JO - Journal of Lie Theory
PY - 2023
SP - 641
EP - 662
VL - 33
IS - 2
UR - http://geodesic.mathdoc.fr/item/JOLT_2023_33_2_a7/
ID - JOLT_2023_33_2_a7
ER -
%0 Journal Article
%A Qinxiu Sun
%A Shan Chen
%T Representations and Cohomologies of Differential Lie-Yamaguti Algebras with any Weights
%J Journal of Lie Theory
%D 2023
%P 641-662
%V 33
%N 2
%U http://geodesic.mathdoc.fr/item/JOLT_2023_33_2_a7/
%F JOLT_2023_33_2_a7
