Examples
1. The set of self-adjoint real, complex, or quaternionic matrices with multiplication
form a special Jordan algebra.
2. The set of 3×3 self-adjoint matrices over the non-associative octonions, again with multiplication
- ,
is a 27 dimensional, exceptional Jordan algebra. Its automorphism group is related to the exceptional Lie group F₄. Since over the real numbers this is the only exceptional Jordan algebra, it is often referred to as "the" exceptional Jordan algebra. It was the first example of an Albert algebra.
Read more about this topic: Jordan Algebra
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