Albert algebra

From Citizendium
Revision as of 14:58, 26 October 2008 by imported>Richard Pinch (New article, my own wording from Wikipedia)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search

The Albert algebra is the set of 3×3 self-adjoint matrices over the octonions with binary operation

where denotes matrix multiplication.

The operation is commutative but not associative. It is an example of an exceptional Jordan algebra. Because most other exceptional Jordan algebras are constructed using this one, it is often referred to as "the" exceptional Jordan algebra.