Cayley-Dickson and Clifford Algebras as Twisted Group Algebras

2011/07/07 by John W. Bales, Bales, John W.
Mathematics · #Algebraic and Geometric Analysis #FOS: Mathematics #Mathematical Analysis and Transform Methods #Rings and Algebras (math.RA) #math.RA

paper · pdf · doi:10.48550/arxiv.1107.1375

arxiv created 2011/07/07 · openalex publication_date 2011/07/07 · arxiv updated 2011/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The effect of some properties of twisted groups on the associated algebras, particularly Cayley-Dickson and Clifford algebras. It is conjectured that the Hilbert space of square-summable sequences is a Cayley-Dickson algebra.

Related

• Properly twisted groups and their algebras
• An alternate Cayley-Dickson product
• The twisted group algebra structure of the Cayley-Dickson algebra
• The Clifford Twist
• About some properties of algebras obtained by the Cayley-Dickson process