Representations of Artin algebras

• Grant number: 22/02403-4
• Support Opportunities: Regular Research Grants
• Start date: July 01, 2022
• End date: June 30, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Flavio Ulhoa Coelho
• Grantee: Flavio Ulhoa Coelho
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

This project focuses on the area of Representations of algebras of Artin and is a continuity of the work that we have been developing in the last 30 years. In general, research in this area encompasses the study and classification of algebras from an in-depth analysis of the respective module categories. To this end, several methodologies have beendeveloped in the last 40 years, bringing applications new procedures of category theory, combinatorics, algebraic geometry, invariant theory and, more recently, with its connection to Cluster algebras. We mentioned, for example, the Auslander-Reiten and tilting theories (see project attachment for more details). In particular, we will continue to focus mainly on problems involving the Auslander-Reiten quivers (with emphasis on its structure and on the composites of irreducible morphisms) and homological issues (tilting theory, the representation dimension and classes of algebras defined from homological dimensions). (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)

CHUST, VIKTOR; COELHO, FLAVIO U.. Representations of generalized bound path algebras. SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, v. N/A, p. 22-pg., 2023-05-15. (18/18123-5, 20/13925-6, 22/02403-4)