Definition:Star-Algebra

Definition

Let $A = \struct {A_F, \oplus}$ be an unitary division algebra.

Let $A$ have a mapping $*: A_F \to A_F$ such that:

$\forall a \in A_F: \paren {a^*}^* = a$

$\forall a, b \in A_F: \paren {a \oplus b}^* = b^* \oplus a^*$

Then $A$ is a $*$-algebra (usually voiced star-algebra).

The mapping $*: A_F \to A_F$ is a conjugation on $A$.

Also see

• Results about star-algebras can be found here.

Sources

• John C. Baez: The Octonions (2002): 2.2 The Cayley-Dickson Construction