Structures and representations of algebraic systems and their applications

• Grant number: 24/14914-9
• Support Opportunities: Research Projects - Thematic Grants
• Start date: July 01, 2025
• End date: June 30, 2030
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Ivan Chestakov
• Grantee: Ivan Chestakov
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Pesquisadores principais: Alexandre Grichkov ; Dessislava Hristova Kochloukova ; Eduardo do Nascimento Marcos ; Plamen Emilov Kochloukov
• Associated researchers: Adriano Adrega de Moura ; Alexandr Kornev ; Angelo Calil Bianchi ; Artem Lopatin ; Claudemir Fideles Bezerra Júnior ; Daniel Levcovitz ; Dimas José Gonçalves ; Felipe Yukihide Yasumura ; Gilson Reis dos Santos Filho ; Henrique Guzzo Junior ; Hugo Luiz Mariano ; Juan Carlos Gutiérrez Fernández ; Kostiantyn Iusenko ; Lucia Satie Ikemoto Murakami ; Luis Enrique Ramírez ; Pedro Souza Fagundes ; Thiago Castilho de Mello ; Tiago Rodrigues Macedo

Abstract

The main part of the project will be devoted to associative, Lie and Jordan algebras and superalgebras and their representations. In addition, alternative and Malcev algebras and superalgebras, Moufang loops and several generalizations will be considered. The main topics are: 1) Representations of Kac-Moody algebras; 2) Homological and homotopic properties and discrete group theory, pro-p groups and Lie algebras; 3) Alternative and Jordan algebras and their generalizations; 4) Loops, non-associative algebras, their representations and applications; 5) Algebras with polynomial identities; 6) Representations of Artin algebras. (AU)