Journal of Lie Theory 33 (2023), No. 2, 547--566
Copyright Heldermann Verlag 2023
Cohomologies and Deformations of Pre-Lie-Morphism Triples
Yibo Wang
School of Mathematics and Statistics, Northeast Normal University, Changchun, China
wangyb843@nenu.edu.cn
Shilong Zhang
College of Science, Northwest A & F University, Yangling, Shaanxi, China
shlzhang11@163.com
Jiefeng Liu
School of Mathematics and Statistics, Northeast Normal University, Changchun, China
liujf534@nenu.edu.cn
A (pre-)Lie-morphism triple consists of two (pre-)Lie algebras and a (pre-)Lie algebra homomorphism between them. We give cohomologies of pre-Lie-morphism triples and show that the cohomology of a pre-Lie-morphism triple can be deduced from a cohomology of the Lie-morphism triple. As applications of cohomologies of pre-Lie-morphism triples, we study linear deformations and formal deformations of pre-Lie-morphism triples.
Keywords: Pre-Lie morphism triple, cohomology, deformation.
MSC: 17B60, 20G10.
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