Clifford algebras obtained by twisting of group algebras

2000/11/07 by Helena Albuquerque, H. Albuquerque, Shahn Majid +3
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #hep-th #math-ph #math.MP #math.QA

paper · pdf · doi:10.48550/arxiv.math/0011040

16 pages latex, no figures

arxiv created 2000/11/07 · openalex publication_date 2000/11/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the construction and properties of Clifford algebras by a similar manner as our previous construction of the octonions, namely as a twisting of group algebras of Z₂ⁿ by a cocycle. Our approach is more general than the usual one based on generators and relations. We obtain in particular the periodicity properties and a new construction of spinors in terms of left and right multiplication in the Clifford algebra.

Related

• Expository paper on Clifford algebras ,representations , and the octonion algebra
• Clifford Algebras, Clifford Groups, and a Generalization of the Quaternions
• On Clifford Algebras and Related Finite Groups and Group Algebras
• The Clifford Twist
• Construction of exceptional Lie algebra G2 and non-associative algebras using Clifford algebra