2017/07/06 by Garret Sobczyk, Sobczyk, Garret · 1 citation
Mathematics · Physics and Astronomy · #15A63 #15A66 #81R05 #81R25 #Advanced Mathematical Theories and Applications #Algebraic and Geometric Analysis #FOS: Mathematics #General Mathematics (math.GM) #Mathematics and Applications #math.GM #msc:15A63 #msc:15A66 #msc:81R05 #msc:81R25
paper · pdf · doi:10.48550/arxiv.1707.02338
This new version shows how Cartan periodicity of Clifford algebras is related to Bott periodicity of homotopy groups and Hurwitz-Radon numbers. It also corrects a number of typos and adds a new section. 15 pages, 6 tables
openalex publication_date 2017/07/06 · arxiv created 2017/07/19 · arxiv updated 2017/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Geometric number systems, obtained by extending the real number system to include new anticommuting square roots of +1 and -1, provide a royal road to higher mathematics by largely sidestepping the tedious languages of tensor analysis and category theory. The well known consistency of real and complex matrix algebras, together with Cartan-Bott periodicity, firmly establishes the consistency of these geometric number systems, often referred to as Clifford algebras. The geometrization of the real number system is the culmination of the thousands of years of human effort at developing ever more sophisticated and encompassing number systems underlying scientific progress and advanced technology in the 21st Century. Complex geometric algebras are also considered.