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Functors Induced by Cauchy Extension of C$^ast$-algebras

Journal: Sahand Communications in Mathematical Analysis (Vol.14, No. 1)

Publication Date:

Authors : ; ;

Page : 27-53

Keywords : Pre-C$^ast$- algebras; Extensions of C$^ast$- algebras; Exact functors; Cauchy extension;

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In this paper, we give three functors $mathfrak{P}$, $[cdot]_K$ and $mathfrak{F}$ on the category of C$^ast$-algebras. The functor $mathfrak{P}$ assigns to each C$^ast$-algebra $mathcal{A}$ a pre-C$^ast$-algebra $mathfrak{P}(mathcal{A})$ with completion $[mathcal{A}]_K$. The functor $[cdot]_K$ assigns to each C$^ast$-algebra $mathcal{A}$ the Cauchy extension $[mathcal{A}]_K$ of $mathcal{A}$ by a non-unital C$^ast$-algebra $mathfrak{F}(mathcal{A})$. Some properties of these functors are also given.  In particular, we show that the functors $[cdot]_K$ and $mathfrak{F}$ are exact and the functor $mathfrak{P}$ is normal exact.

Last modified: 2019-04-28 14:13:45