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
Famous quotes containing the word examples:
“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
—G.C. (Georg Christoph)
“No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
—André Breton (1896–1966)
“There are many examples of women that have excelled in learning, and even in war, but this is no reason we should bring ‘em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.”
—Bernard Mandeville (1670–1733)