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.


Sources