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Clifford algebras and classification of spinors from the bilinear covariants

Grant number: 12/10794-1
Support type:Scholarships in Brazil - Scientific Initiation
Effective date (Start): September 01, 2012
Effective date (End): August 31, 2013
Field of knowledge:Physical Sciences and Mathematics - Mathematics
Principal Investigator:Roldão da Rocha Junior
Grantee:Rodolfo Akio Uchida
Home 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 definition.This project will introduce to student 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.