Matrix groups

• Grant number: 05/01742-4
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Effective date (Start): September 01, 2005
• Effective date (End): August 31, 2006
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Ronan Antonio dos Reis
• Grantee: Sylaine Santana de Souza
• Host Institution: Faculdade de Ciências e Tecnologia (FCT). Universidade Estadual Paulista (UNESP). Campus de Presidente Prudente. Presidente Prudente , SP, Brazil

Abstract

In this work, the student will begin in research in the area of Lie Theory through the study of the matrix Lie groups. A proposed problem is to verify eventual isomorphisms between groups of small dimensions, like Sp(1) and SO(3). To solve the problem, it will be necessary, at least, to study the followings topics: Groups, Fields, Matrix Groups, Inner Products, Orthogonal Groups, The question of the Isomorphism, Reflections in Rn, Exponential and Logarithm of matrix, One-Parameter Subgroups, Matrix Lie Algebras, Curves in Vector Spaces, Smooth Homomorphisms , Centers and Quotiente of Matrix Groups.