In mathematics, a *-algebra is an associative algebra over the field of complex numbers with an antilinear antiautomorphism * : A->A which is an involution. More precisely, * is required to satisfy the following properties: for all a,b in A, and z a complex number,

The field of complex numbers C is a *-algebra with * being complex conjugation.

An algebra homomorphism f : A->B is a *-homomorphism if, in addition, is compatible with the involutions of A and B. What this means is that

• f(a ^* ) = f(a) ^* for all a in A.

If a*=a, then a is called self-adjoint.

See also B* algebra, C* algebra, operator algebra, self-adjoint.