Zhuang Niu,Department of Mathematics, University of Wyoming, Laramie, Wyoming, 82071 USA; e-mail: zniu@uwyo.edu

Abstract/Résumé:

Motivated by Huaxin Lin’s axiomatization of AH-algebras, the class of TASI-algebras is introduced as the class of unital C*-algebras which can be tracially approximated by splitting interval algebras—certain sub-C*-algebras of interval algebras. It is shown that the class of simple separable nuclear TASI-algebras satisfying the UCT is classified by the Elliott invariant. As a consequence, any such TASI-algebra is then isomorphic to an inductive limit of splitting interval algebras together with certain homogeneous C*-algebras—so it is an ASH-algebra.

Une classe de C*-algèbres qui généralisent la classe bien connue TAI de Lin est considérée—basées sur, au lieu de l’intervalle, ce qui pourrait s’appeler l’intervalle fendu (“splitting interval”), de sorte que l’on les appelle la classe TASI. On montre que la classe de C*-algèbres TASI qui sont simples, nucléaires, et à élément unité, qui vérifient le théorème à coefficients universels (UCT), peuvent se classifier d’après l’invariant d’Elliott.

Keywords: Classification of simple C*-algebras, inductive limits of sub-homogeneous C*- algebras, tracially approximate splitting interval algebras

AMS Subject Classification: Classifications of $C^*$-algebras; factors 46L35

PDF(click to download): A Classification of Tracially Approximate Splitting Interval Algebras. III. Uniqueness Theorem and Isomorphism Theorem

Zhuang Niu, Department of Mathematics, University of Wyoming, Laramie, Wyoming, 82071 USA; e-mail: zniu@uwyo.edu

Abstract/Résumé:

Motivated by Huaxin Lin’s axiomatization of AH-algebras, the class of TASI-algebras is introduced as the class of unital C*-algebras which can be tracially approximated by splitting interval algebras—certain sub-C*-algebras of interval algebras. It is shown that the class of simple separable nuclear TASI-algebras satisfying the UCT is classified by the Elliott invariant. As a consequence, any such TASI-algebra is then isomorphic to an inductive limit of splitting interval algebras together with certain homogeneous C*-algebras—so it is an ASH-algebra.

Une classe de C*-algèbres qui généralisent la classe bien connue TAI de Lin est considérée—basées sur, au lieu de l’intervalle, ce qui pourrait s’appeler l’intervalle fendu ("splitting interval"), de sorte que l’on les appelle la classe TASI. On montre que la classe de C*-algèbres TASI qui sont simples, nucléaires, et à élément unité, qui vérifient le théorème à coefficients universels (UCT), peuvent se classifier d’après l’invariant d’Elliott.

Keywords: Classification of simple C*-algebras, inductive limits of sub-homogeneous C*- algebras, tracially approximate splitting interval algebras

AMS Subject Classification: Classifications of $C^*$-algebras; factors 46L35

PDF(click to download): A Classification of Tracially Approximate Splitting Interval Algebras. II. Existence Theorem

Zhuang Niu, Department of Mathematics, University of Wyoming, Laramie, Wyoming, USA 82071; e-mail: zniu@uwyo.edu

Abstract/Résumé:

Motivated by Huaxin Lin’s axiomatization of AH-algebras, the class of TASI-algebras is introduced as the class of unital C*-algebras which can be tracially approximated by splitting interval algebras—certain sub-C*-algebras of interval algebras. It is shown that the class of simple separable nuclear TASI-algebras satisfying the UCT is classified by the Elliott invariant. As a consequence, any such TASI-algebra is then isomorphic to an inductive limit of splitting interval algebras together with certain homogeneous C*-algebras—so it is an ASH-algebra.

Une classe de C*-algèbres qui généralisent la classe bien connue TAI de Lin est considérée—basées sur, au lieu de l’intervalle, ce qui pourrait s’appeler l’intervalle fendu (“splitting interval”), de sorte que l’on les appelle la classe TASI. On montre que la classe de C*-algèbres TASI qui sont simples, nucléaires, et à élément unité, qui vérifient le théorème à coefficients universels (UCT), peuvent se classifier d’après l’invariant d’Elliott.

Keywords: Classification of simple C*-algebras, inductive limits of sub-homogeneous C*- algebras, tracially approximate splitting interval algebras

AMS Subject Classification: Classifications of $C^*$-algebras; factors 46L35

PDF(click to download): A Classification of Tracially Approximate Splitting Interval Algebras~~I. The Building Blocks and the Limit Algebras