Normed Division Algebra - Composition Algebras

Composition Algebras

Normed division algebras are a special case of composition algebras. Composition algebras are unital algebras with a multiplicative quadratic form. General composition algebras need not be division algebras, however—they may contain zero divisors. Over the real numbers this gives rise to three additional algebras: the split-complex numbers, the split-quaternions, and the split-octonions.