Classical groups in the Quantum Clifford algebras formalism

• Grant number: 12/07710-0
• Support Opportunities: Scholarships abroad - Research Internship - Master's degree
• Start date: September 01, 2012
• End date: September 30, 2012
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Roldão da Rocha
• Grantee: Ícaro Gonçalves
• Supervisor: Rafal Ablamowicz
• Host Institution: Centro de Matemática, Computação e Cognição (CMCC). Universidade Federal do ABC (UFABC). Ministério da Educação (Brasil). Santo André , SP, Brazil
• Institution abroad: Tennessee Tech University (TTU), United States
• Associated to the scholarship: 11/04918-7 - Quantum Clifford algebras and associated Hopf algebras, BP.MS

Abstract

The main purpose of this research is to investigate the classical groups, especially the Pin and Spin groups within the quantum Clifford algebras formalism and their representations, and to find out the pinor and spinor spaces that carries the Spin group representation. We have been working on the quantum Clifford algebras formalism for one year according to the prior project FAPESP 2011/04918-7, and we have already shown what happens when one deforms the associated bilinear form related to the Clifford algebra. Although works from Chevalley, da Rocha, Ablamowicz and Fauser have given clarity for this subject, the classification of spinors and the construction of the Pin and Spin groups lack a complete and formal approach. Our aim is that, with Rafal Ablamowicz’s collaboration well established, we may seek and find a solution to these open problems in Clifford algebras: a complete study of Pin and Spin groups within quantum Clifford algebras and their implications throughout the classification of spinors. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

ABLAMOWICZ, RAFAL; GONCALVES, ICARO; DA ROCHA, ROLDAO. Bilinear covariants and spinor fields duality in quantum Clifford algebras. Journal of Mathematical Physics, v. 55, n. 10, OCT 2014. (11/04918-7, 12/07710-0)