covering dimension — 1 articles found.

A note on subhomogeneous $C^*$-algebras

C. R. Math. Rep. Acad. Sci. Canada Vol. 28 (3) 2006, pp. 91–96
Vol.28 (3) 2006
Ping Wong Ng; Wilhelm Winter Details
(Received: 2006-01-22 )
(Received: 2006-01-22 )

Ping Wong Ng, The Fields Institute for Research in Mathematical Sciences, 222 College Street, Toronto, Ontario M5T 3J1; email: pwn@erdos.math.unb.ca

Wilhelm Winter, Mathematisches Institut der Universitat Munster, Einsteinstr. 62, D-48149 Munster, Germany; email: wwinter@math.uni-uenster.de

Abstract/Résumé:

We show that finitely generated subhomogeneous \(C^*\)-algebras have finite decomposition rank. As a consequence, any separable ASH \(C^*\)-algebra can be written as an inductive limit of subhomogeneous \(C^*\)-algebras each of which has finite decomposition rank.

It then follows from work of H. Lin and the second author that the class of simple unital ASH algebras which have real rank zero and absorb the Jiang-Su algebra tensorially satisfies the Elliott conjecture.

Nous établissons qu’une \(C^*\)-algèbre sous-homogène engendrée par un nombre fini d’éléments est de rang de décomposition fini. Par conséquence toute ASH \(C^*\)-algèbre peut être décrite comme limite inductive de \(C^*\)-algèbres sous-homogènes chacune desquelles est de rang de dècomposition fini.

Les traveaux de H. Lin et du deuxième auteur nous permettent d’en déduire que la classe d’AHS algèbres à élément unité qui sont simple, de rang réel zéro et qui absorbent tensoriellement l’algèbre de Jiang et Su, satisfait à la conjecture d’Elliott.

Keywords: approximately subhomogeneous C∗-algebras, covering dimension

AMS Subject Classification: General theory of $C^*$-algebras 46L05

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