Clifford algebras and classification of spinors from the bilinear covariants

• Grant number: 12/10794-1
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: September 01, 2012
• End date: August 31, 2013
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Roldão da Rocha
• Grantee: Rodolfo Akio Uchida
• Host Institution: Centro de Matemática, Computação e Cognição (CMCC). Universidade Federal do ABC (UFABC). Ministério da Educação (Brasil). Santo André , SP, Brazil

Abstract

From the fundamental concepts involving Clifford algebras and their representations, we shall investigate the groups of rotations and their double covering in Euclidean space. The main objective of this project, at first sight, is to introduce the fundamentals related to the groups Spin (3) and Spin (1, 3), the groups respectively related to the three-dimensional euclidean space and to space-time, and further investigate some properties concerning the subsequent spaces which carry representations of these groups. Later we will investigate the bilinear covariants associated with such spinors, after introducing such objects through two possible definitions and equivalents of spinors, algebraic and classical definitions. This project will introduce to students fundamental concepts for a later study of various advanced topics, such as the classification of Clifford algebras and their representation, as well as the periodicity theorem and applications.(AU)