Octonions as Clifford-like algebras

DOI10.1016/j.jalgebra.2024.01.020arXiv2310.09972WikidataQ129409891 ScholiaQ129409891MaRDI QIDQ6153584

Jonathan D. H. Smith, Mitchell D. Ashburn, Connor M. Depies

Publication date: 14 February 2024

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2310.09972

zbMATH Keywords

quadratic algebraClifford algebraoctonionsalternative algebraCayley-Dickson algebra

Mathematics Subject Classification ID

Alternative rings (17D05) Nonassociative division algebras (17A35) Quadratic algebras (but not quadratic Jordan algebras) (17A45)

Cites Work

• A series of algebras generalizing the octonions and Hurwitz-Radon identity
• Clifford algebras and Euclid's parametrization of Pythagorean triples
• A survey on paracomplex geometry
• Veronese representation of projective Hjelmslev planes over some quadratic alternative algebras
• Quadratic forms permitting composition
• William Kingdon Clifford (1845–1879)
• Quadratic alternative algebras
• The octonions
• Quadratic Division Algebras
• On the Algebras Formed by the Cayley-Dickson Process
• Alternative algebras over an arbitrary field
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item