| Grant number: | 22/12963-7 |
| Support Opportunities: | Scholarships in Brazil - Doctorate |
| Start date: | January 01, 2023 |
| End date: | 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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