PlanetPhysics/Category of C Algebras

\newcommand{\sqdiagram}[9]{Failed to parse (unknown function "\diagram"): {\displaystyle \diagram #1 \rto^{#2} \dto_{#4}& \eqno{\mbox{#9}}} }

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 Sources

edit

[1] [2]

References

edit
  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.