Introduction to Lie Algebras

• Grant number: 22/01380-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: April 01, 2022
• End date: February 29, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Fabio Ferrari Ruffino
• Grantee: Vitor Schiavuzzo Ferreira
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

The main aim of the present project consists in introducing the candidate to the theory of finite-dimensional Lie algebras. He will start from the definition of Lie algebra and he will conclude with the classification of simple complex algebras through the corresponding root systems and Dynkin diagrams. Since the concept of representation is particularly relevant in this theory, in the first part of the work the candidate will also study the main notions about finite-group representations and character theory.(AU)