Non commutative rings and applications

• Grant number: 20/16594-0
• Support Opportunities: Research Projects - Thematic Grants
• Duration: June 01, 2021 - May 31, 2026
• 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 researchers: Javier Sanchez Serda ; Raul Antonio Ferraz ; Vitor de Oliveira Ferreira
• Associated grant(s): 23/14066-5 - Partial actions, Galois cohomology and seven term exact sequences, AV.EXT; 22/15567-5 - PI-ALGEBRAS, FUNDAMENTAL ALGEBRAS AND APPLICATIONS, AV.EXT; 22/13508-1 - Crossed Product Codes, AV.EXT
• Associated scholarship(s): 22/12963-7 - (Co)homology and partial actions, BP.DR; 22/11166-6 - Some topics on groupoid graded rings, BP.DR; 22/00953-7 - Cohomology, globalization and related topics, BP.PD; 19/08659-8 - Lie algebras: isomorphisms and actions, BP.PD

Abstract

We intend to continue the research on non commutative rings and applications. The research group has been working in this direction for quitea long time and has already obtained expressive results that are frequently quoted in the literature. The subjects that will be the object of our research in the forth coming period are, among others: the structure of group algebras and its applications to the theory of error-correcting codes. We expect to study the relations among several classes of codes - cyclic, abelian, metabelian, nilpotent, etc. -and to exibit efficient codes constructed in this way; the structure of division rings and, in particular, the existence of free objects (groups, algebras, group algebras) in division rings infinite dimensional over their centers. Apply methods of microlocalization to generalize Cohn's localization theory to graded division rings; study cohomologies based on partial actions and in partial group algebras, the problem of the globalization of partial cohomology, extension of rings related to partial actions, galois theory of partial actions and applications of the theory to semigroups, symbolic dynamics, and other classes of algebras; hopf algebras and their non commutative invariants; rings with polynomial identities, particularly fundamental álgebras and growth problems. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

ABRAMS, G.; DOKUCHAEV, M.; NAM, T. G.. Realizing corners of Leavitt path algebras as Steinberg algebras, with corresponding connections to graph C{*}-algebras. Journal of Algebra, v. 593, p. 72-104, MAR 1 2022. (20/16594-0, 18/06538-6)