Groups and noncommutative algebra: interactions and applications
Galois Theory, profinite groups and applications in quadratic forms
Grant number: | 09/52665-0 |
Support Opportunities: | Research Projects - Thematic Grants |
Duration: | November 01, 2009 - October 31, 2014 |
Field of knowledge: | Physical Sciences and Mathematics - Mathematics - Algebra |
Principal Investigator: | Francisco Cesar Polcino Milies |
Grantee: | Francisco Cesar Polcino Milies |
Host Institution: | Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil |
Pesquisadores principais: | Jairo Zacarias Goncalves ; Mikhailo Dokuchaev |
Associated grant(s): | 13/19544-0 - Partial actions and partial representations,
AV.EXT 12/20425-3 - Twisted partial actions and the Brauer group, AV.BR 12/00878-3 - Some classes of semi-perfect rings, AV.EXT + associated grants - associated grants |
Associated scholarship(s): | 12/20138-4 - About Units of Group Rings and Codes,
BP.PD 12/07610-6 - Partial Schur Multiplier, cohomology and related topics, BP.PD 12/01554-7 - Partial actions and representations, cohomology and globalization, BP.PD |
Abstract
We intend to continue the research on the interactions between group theory and non-commutative algebra, and some of its applications. Our group has worked in these directions for quite some time and has already obtained results that are frequently quoted in the literature. Specific subjects to be studied on the period are, among others: the structure of the group of units of a group ring, determining generators of the free complement, in the case of finite abelian groups, and free pairs of generators, in the general case. We shall also study symmetric and skew symmetric elements in a group algebra. The structure of the group of units of a division ring and the existence of free pairs of special type. Study of globalization of partial actions, generalized crossed products, isomorphism of partial group algebras, partial actions and co-actions of Hopf algebras, partial projective representations and co-homology based on partial actions. Study of codes: cyclic, abelian, metacyclic, etc., using techniques of finite group algebras. (AU)
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