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Entree


(Co)homology of partial smash products

Texto completo
Autor(es):
Dokuchaev, Mikhailo ; Jerez, Emmanuel
Número total de Autores: 2
Tipo de documento: Artigo Científico
Fonte: Journal of Algebra; v. 652, p. 45-pg., 2024-05-08.
Resumo

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)

Processo FAPESP: 20/16594-0 - Anéis não comutativos e aplicações
Beneficiário:Francisco Cesar Polcino Milies
Modalidade de apoio: Auxílio à Pesquisa - Temático
Processo FAPESP: 22/12963-7 - (Co)homologia e ações parciais
Beneficiário:Emmanuel Jerez Usuga
Modalidade de apoio: Bolsas no Brasil - Doutorado