PlanetPhysics/Category of C Algebras

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Let  be two C*-algebras. Then a -homomorphism

is defined as a C*-algebra homomorphism which respects involutions, that is:

Note: If `by abuse of notation' one uses to denote both and , then any -homomorphism commutes with , i.e., .

The category whose objects are -algebras and whose morphisms are -homomorphisms is called the category of -algebras or the -algebra category.

{\mathbf Remark:} Note that homomorphisms between -algebras are automatically continuous.

All SourcesEdit



  1. Kustermans, J., C*-algebraic Quantum Groups arising from Algebraic Quantum Groups, Ph.D. Thesis, K.U.Leuven, 1997.
  2. Sheu, A.J.L., Compact Quantum Groups and Groupoid C*-Algebras, J. Funct. Analysis 144 (1997), 371-393.