Cohomologies and deformations of coassociative coderivations
Rings and Algebras
2023-01-31 v1
Abstract
The motivation of this paper is to construct a deformation theory of coderivations of coassociative coalgebras. We introduce a notion of a Coder pair, that is, a coassociative coalgebra with a coderivation. Then we define a proper corepresentation of a Coder pair and study the corresponding cohomology. Finally, we show that a Coder pair is rigid, provided that the second cohomology group is trivial and point out that a deformation of finite order is extensible to higher order deformations if the obstruction class, which is defined to be in the third cohomology group, is trivial.
Cite
@article{arxiv.2301.12114,
title = {Cohomologies and deformations of coassociative coderivations},
author = {Lei Du and Yashuang Ma and Jiangnan Xv and Yanhong Bao},
journal= {arXiv preprint arXiv:2301.12114},
year = {2023}
}
Comments
To appear in Communications in Algebra