2005/03/08 by Michael Rios, Rios, Michael
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Physical sciences #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.math-ph/0503015
LaTeX, 11 pages, misprints corrected
openalex publication_date 2005/03/08 · arxiv created 2005/07/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We elucidate the geometry of matrix models based on simple formally real Jordan algebras. Such Jordan algebras give rise to a nonassociative geometry that is a generalization of Lorentzian geometry. We emphasize constructions for the exceptional Jordan algebra and the exceptional Jordan C*-algebra and describe the projective spaces related to the exceptional cubic matrix model and the E6 matrix model. The resulting projective spaces are shown to be exceptional versions of projective twistor space, thus revealing the existence of exceptional twistor string theories that are dual to octonionic matrix models.