Uintell Mathematics Encyclopedia

octonions

Hypercomplex numbers (cf. Hypercomplex number), namely, the elements of the 8-dimensional algebra over the field of real numbers (the Cayley algebra), also termed octonions. They were first considered by A. Cayley. The Cayley algebra may be derived via the Cayley–Dickson process from the algebra of quaternions (see Cayley–Dickson algebra; Quaternion). It is the only 8-dimensional real alternative algebra without zero divisors (see Frobenius theorem). The Cayley algebra is an algebra with unique division and with an identity; it is alternative, non-associative and non-commutative.

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