Division Algebras
There are only three associative division algebras over the reals - the real numbers, the complex numbers and the quaternions. The only non-associative division algebra is the algebra of octonions. The octonions are connected to a wide variety of exceptional objects. For example the exceptional formally real Jordan algebra is the Albert algebra of 3 by 3 self-adjoint matrices over the octonions.
Read more about this topic: Exceptional Object
Famous quotes containing the word division:
“Slow, slow, fresh fount, keep time with my salt tears;
Yet slower yet, oh faintly gentle springs:
List to the heavy part the music bears,
“Woe weeps out her division when she sings.”
Droop herbs and flowers;
Fall grief in showers;
“Our beauties are not ours”:
Oh, I could still,
Like melting snow upon some craggy hill,
Drop, drop, drop, drop,
Since nature’s pride is, now, a withered daffodil.”
—Ben Jonson (1572–1637)