Cayley-Dickson and Clifford Algebras as Twisted Group Algebras
John W. Bales
TL;DR
This paper explores the properties of twisted groups and their influence on Cayley-Dickson and Clifford algebras, proposing a conjecture that the Hilbert space of square-summable sequences forms a Cayley-Dickson algebra.
Contribution
It investigates the impact of twisted group properties on algebra structures and introduces a conjecture linking Hilbert spaces to Cayley-Dickson algebras.
Findings
Analysis of twisted group properties on algebra structures
Conjecture that Hilbert space of square-summable sequences is a Cayley-Dickson algebra
Insights into algebraic properties influenced by group twists
Abstract
The effect of some properties of twisted groups on the associated algebras, particularly Cayley-Dickson and Clifford algebras. It is conjectured that the Hilbert space of square-summable sequences is a Cayley-Dickson algebra.
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Taxonomy
TopicsAlgebraic and Geometric Analysis · Mathematical Analysis and Transform Methods