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Encyclopedia > Star algebra

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.


  Results from FactBites:
 
Deformation Quantization Homepage: Selected (1772 words)
Soon later Fedosov gave his geometric construction of star products on symplectic manifolds in 1985 which was unfortunately unnoticed till the early nineties, see his book for a detailed description [fedosov:1996a].
Roughly, a strict deformation quantization of a (Poisson) C* algebra A is the data of a continuous field of C* algebras over an interval containing zero.
This algebraic GNS construction is also the starting point for a general representation theory of the deformed algebras.
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