Introduction to the geometry of Lie groups

• Grant number: 17/01597-1
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: July 01, 2017
• End date: December 31, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: José Régis Azevedo Varão Filho
• Grantee: Daniel Aguilar Gomes
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

In this project the student will study the geometric implications induced by the complex numbers and quarternions. In addition the student must learn some basic concepts of groups and then apply it to groups of matrices. In particular it will be studied the generalized groups of rotations, studying their various properties, among them dynamical ones. For other classical groups will be made the study of maximal torus, centers, simplicity and topological properties. Finally, the study of the exponential map and the space tangent to the neutral element is started. (AU)