Beyond Octonions
Khaled Abdel-Khalek (Lecce, Italy)
TL;DR
This paper explores the structure of Clifford Algebras over non-ring division algebras and demonstrates how real field projections recover the Attiyah-Bott-Shapiro classification.
Contribution
It introduces a novel perspective on Clifford Algebras over non-ring division algebras and links them to established classifications via real projections.
Findings
Clifford Algebras over non-ring division algebras are structurally analyzed.
Projection over the real field yields the Attiyah-Bott-Shapiro classification.
Provides a new framework connecting algebraic structures to classification results.
Abstract
We investigate Clifford Algebras structure over non-ring division algebras. We show how projection over the real field produces the standard Attiyah-Bott-Shapiro classification.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Rings, Modules, and Algebras