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 $A$.