Connections between Algebra and Geometry: an introduction to Clifford algebras

• Grant number: 13/21729-9
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: February 01, 2014
• End date: December 31, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Jaime Edmundo Apaza Rodriguez
• Grantee: Joél Faria Junior
• Host 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 (including Differential Geometry) are presented in the way " isolated ", without being presented their connections with other areas. For example, in Abstract Algebra, usually no is the address Groups Linear and 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.