Scholarship 22/12963-7 - Ação parcial, Cohomologia - BV FAPESP
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(Co)homology and partial actions

Grant number: 22/12963-7
Support Opportunities:Scholarships in Brazil - Doctorate
Start date until: January 01, 2023
End date until: August 31, 2024
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Algebra
Principal Investigator:Mikhailo Dokuchaev
Grantee:Emmanuel Jerez Usuga
Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Associated research grant:20/16594-0 - Non commutative rings and applications, AP.TEM

Abstract

The project will be dedicated to the study of Hochschild (co)homology and cyclic (co)homology of partial crossed products and their relation with the partial group (co)homology. More precisely, given a partial action of a group $G$ on an algebra $A,$ we intent to prove the existence of a spectral sequence which relates the Hochschild homology of the partial crossed product $A \ast G$ with the partial homology of $G$ and the Hochschild homology of $A,$ obtaining a homological analogue of a recent cohomological result. Moreover, we plan to try to obtain a decomposition of the Hochschild (co)homology of the partial crossed product $A \ast G$into a direct sum of the (co)homologies of simplicial complexes related to the conjugacy classes of $G.$ These problems will be discussed also for the more general case of a partial action of a Hopf algebra $H$ on an algebra $A$.We will also study the convergence of the spectral sequences obtained from the various filtrations constructed from a natural filtration of the Exel's semigroup $S(G)$ associated to a group $G$. Furthermore, we plan to consider the possibility to generalize the Lyndon-Hochschild-Serrespectral sequence for the context of the partial group cohomology.

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Academic Publications
(References retrieved automatically from State of São Paulo Research Institutions)
USUGA, Emmanuel Jerez. Partial actions and homology. 2024. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) São Paulo.

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