Definition:Star-Algebra
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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.