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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


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.

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