(Co)Homology of Partial Smash Products
Rings and Algebras
2023-11-29 v1 Representation Theory
Abstract
Given a cocommutative Hopf algebra over a commutative ring and a symmetric partial action of on a -algebra we obtain a first quadrant Grothendieck spectral sequence converging to the Hochschild homology of the smash product involving the Hochschild homology of and the partial homology of An analogous third quadrant cohomological spectral sequence is also obtained. The definition of the partial (co)homology of under consideration is based on the category of the partial representations of A specific partial representation of on a subalgebra of the partial ``Hopf" algebra is involved in the definition and we construct a projective resolution of
Keywords
Cite
@article{arxiv.2311.16990,
title = {(Co)Homology of Partial Smash Products},
author = {Mikhailo Dokuchaev and Emmanuel Jerez},
journal= {arXiv preprint arXiv:2311.16990},
year = {2023}
}