| Full text | |
| Author(s): |
Dokuchaev, Mikhailo
;
Jerez, Emmanuel
Total Authors: 2
|
| Document type: | Journal article |
| Source: | Journal of Algebra; v. 652, p. 45-pg., 2024-05-08. |
| Abstract | |
Given a cocommutative Hopf algebra H over a commutative ring K and a symmetric partial action of H on a K -algebra A, we obtain a first quadrant Grothendieck spectral sequence converging to the Hochschild homology of the smash product A# H, involving the Hochschild homology of A and the partial homology of H. An analogous third quadrant cohomological spectral sequence is also obtained. The definition of the partial (co)homology of H under consideration is based on the category of the partial representations of H. A specific partial representation of H on a subalgebra B of the partial "Hopf" algebra H par is involved in the definition and we construct a projective resolution of B. (c) 2024 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 20/16594-0 - Non commutative rings and applications |
| Grantee: | Francisco Cesar Polcino Milies |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 22/12963-7 - (Co)homology and partial actions |
| Grantee: | Emmanuel Jerez Usuga |
| Support Opportunities: | Scholarships in Brazil - Doctorate |