Introduction to affine Kac-Moody algebras

• Grant number: 25/05675-3
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: June 01, 2025
• End date: May 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Eder de Moraes Correa
• Grantee: Gabriela Martins dos Santos
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

The main purpose of this scientific initiation project is to introduce the scholarship holder to the study of the theory of Kac-Moody algebras. Aiming at the classification of non-twisted affine Kac-Moody algebras, throughout the development of the project the student will come into contact with the classification theory of finite-dimensional complex semisimple Lie algebras and their respective loop algebras. At the end of the project, the student is expected to have acquired a solid foundation in the fundamentals of the theory of finite-dimensional complex semisimple Lie algebras and their applications in the study of infinite-dimensional Lie algebras and their representations. (AU)