Cohomologies of pre-LieDer pairs and applications
Rings and Algebras
2023-06-23 v1
Abstract
In this paper, we use the higher derived bracket to give the controlling algebra of pre-LieDer pairs. We give the cohomology of pre-LieDer pairs by using the twist -algebra of this controlling algebra. In particular, we define the cohomology of regular pre-LieDer pairs. We study infinitesimal deformations of pre-LieDer pairs, which are characterized by the second cohomology group of pre-LieDer pairs. We also define the cohomology of regular pre-LieDer pairs with coefficients in arbitrary representation and using the second cohomology group to classify abelian extensions of regular pre-LieDer pairs.
Keywords
Cite
@article{arxiv.2306.12425,
title = {Cohomologies of pre-LieDer pairs and applications},
author = {Shanshan Liu and Liangyun Chen},
journal= {arXiv preprint arXiv:2306.12425},
year = {2023}
}