The Jiang-Su algebra revisited

Mikael Rørdam; Wilhelm Winter

The Jiang-Su algebra revisited

Institut for Matematiske Fag

68 Citationer (Scopus)

Abstract

We give a number of new characterizations of the Jiang-Su algebra Z, both intrinsic and extrinsic, in terms of C^*-algebraic, dynamical, topological and K-theoretic conditions. Along the way we study divisibility properties of C^*-algebras, we give a precise characterization of those unital C^*-algebras of stable rank one that admit a unital embedding of the dimension-drop C^*-algebra Z _n, n+1, and we prove a cancellation theorem for the Cuntz semigroup of C^*-algebras of stable rank one.

Originalsprog	Engelsk
Tidsskrift	Journal fur die Reine und Angewandte Mathematik
Vol/bind	642
Sider (fra-til)	129-155
Antal sider	26
ISSN	0075-4102
Status	Udgivet - maj 2010

Citationsformater

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TY - JOUR

T1 - The Jiang-Su algebra revisited

AU - Rørdam, Mikael

AU - Winter, Wilhelm

PY - 2010/5

Y1 - 2010/5

N2 - We give a number of new characterizations of the Jiang-Su algebra Z, both intrinsic and extrinsic, in terms of C*-algebraic, dynamical, topological and K-theoretic conditions. Along the way we study divisibility properties of C*-algebras, we give a precise characterization of those unital C*-algebras of stable rank one that admit a unital embedding of the dimension-drop C*-algebra Z n, n+1, and we prove a cancellation theorem for the Cuntz semigroup of C*-algebras of stable rank one.

AB - We give a number of new characterizations of the Jiang-Su algebra Z, both intrinsic and extrinsic, in terms of C*-algebraic, dynamical, topological and K-theoretic conditions. Along the way we study divisibility properties of C*-algebras, we give a precise characterization of those unital C*-algebras of stable rank one that admit a unital embedding of the dimension-drop C*-algebra Z n, n+1, and we prove a cancellation theorem for the Cuntz semigroup of C*-algebras of stable rank one.

M3 - Journal article

SN - 0075-4102

VL - 642

SP - 129

EP - 155

JO - Journal fur die Reine und Angewandte Mathematik

JF - Journal fur die Reine und Angewandte Mathematik

ER -

The Jiang-Su algebra revisited

Abstract

Fingeraftryk

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