Some identities in algebras obtained by the Cayley-Dickson process
Cristina Flaut, Vitalii Shpakivskyi
TL;DR
This paper proves the Hall identity holds in all Cayley-Dickson algebras and explores conditions under which the converse is true, deepening understanding of algebraic identities in these structures.
Contribution
It establishes the validity of the Hall identity across all Cayley-Dickson algebras and identifies conditions for the converse to hold, advancing algebraic theory.
Findings
Hall identity is valid in all Cayley-Dickson algebras
Conditions identified where the converse of the Hall identity holds
Enhanced understanding of algebraic identities in Cayley-Dickson structures
Abstract
In this paper we will prove that the Hall identity is true in all algebras obtained by the Cayley-Dickson process and, in some conditions, the converse is also true.
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 and Geometric Analysis · Advanced Mathematical Theories and Applications · Parallel Computing and Optimization Techniques