Connections between Algebra and Geometry: An Introduction to Clifford Algebras

• Grant number: 13/21729-9
• Support type: Scholarships in Brazil - Scientific Initiation
• Effective date (Start): February 01, 2014
• Effective date (End): December 31, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Jaime Edmundo Apaza Rodriguez
• Grantee: Joél Faria Junior
• Home Institution: Faculdade de Engenharia (FEIS). Universidade Estadual Paulista (UNESP). Campus de Ilha Solteira. Ilha Solteira , SP, Brazil

Abstract

To main objective this project is to study the interaction between the geometry and Algebra,using for this purpose the language of Quaternions and Clifford Algebras.In general, the current classes of graduate courses of mathematica in Brazil, the disciplines of Algebra Abstract (rings, fields, groups ), as well as the subjects geometry (includingDifferential Geometry ) are presented in the way " isolated ", without being presented theirconnections with other areas. For example, in Abstract Algebra, usually no is the address Groups Linearand their subgroups (Orthogonal groups, Unitary, etc. ), which are good examples of the continues groups, endowed with a geometric structure ( topological). So also in Geometry,perhaps little or no emphasis is given for to action groups over geometric objects.Then the major objective of this project is show by studying some specific cases, the richness and variety of connections that exists between Algebra and Geometry .