Algebras with polynomial identities

• Grant number: 19/22813-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: February 01, 2020
• End date: November 30, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Lucia Satie Ikemoto Murakami
• Grantee: Roger Ramirez Primolan
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 18/23690-6 - Structures, representations, and applications of algebraic systems, AP.TEM

Abstract

The central theme of this project is the theory of associative algebras that satisfy polynomial identities. It is a theory that includes commutative algebras and finite-dimensional algebras, therefore it is sufficiently embracing. In addition, the methods used for its development merge diverse areas such as combinatorics, the structural theory of rings and representations of groups. Special focus will be given to the analytic methods introduced by A. Regev, where the asymptotic growth of codimensions is studied. This is an area that is in full development, which will allow the student to approach the current research developed on the subject. The main fact, however, is the diversity of techniques used, which will provide the student with a broad background, which may be useful in various areas of algebra. For example, a quick preview of how the methods extend to the study of no associative algebras is also programmed. One of the goals is to give the student a good preparation for postgraduate in algebra. (AU)