Theory of Groups and Gabriel's theorem

• Grant number: 20/11159-4
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: January 01, 2021
• End date: December 31, 2021
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Eduardo do Nascimento Marcos
• Grantee: Maria Luiza Rocha Bueno
• 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

We will start with the study of basic theory of groups, after the student get some basic facts on the subject and also in the abstract algebras we will study various notions on the theory of algebras over comutative rings and specially over algebraically closed fields, specially finite dimensional algebras. Notions of equivalence of category of modules and projectivety will be study, them the notion of basic algebra and the classification theorem of Gabriel. This project will prepare the student for the advance study of Theory of representations of algebras.