Tensor Products and Regularity Properties of Cuntz Semigroups (Memoirs of the American Mathematical Society) - Softcover

Antoine, Ramon; Perera, Francesc; Thiel, Hannes

Softcover

ISBN 10: 1470427974 ISBN 13: 9781470427979

Verlag: American Mathematical Society, 2018

Inhaltsangabe

The Cuntz semigroup of a $C^*$-algebra is an important invariant in the structure and classification theory of $C^*$-algebras. It captures more information than $K$-theory but is often more delicate to handle. The authors systematically study the lattice and category theoretic aspects of Cuntz semigroups.

Given a $C^*$-algebra $A$, its (concrete) Cuntz semigroup $\mathrm{Cu}(A)$ is an object in the category $\mathrm{Cu}$ of (abstract) Cuntz semigroups, as introduced by Coward, Elliott and Ivanescu. To clarify the distinction between concrete and abstract Cuntz semigroups, the authors call the latter $\mathrm{Cu}$-semigroups.

The authors establish the existence of tensor products in the category $\mathrm{Cu}$ and study the basic properties of this construction. They show that $\mathrm{Cu}$ is a symmetric, monoidal category and relate $\mathrm{Cu}(A\otimes B)$ with $\mathrm{Cu}(A)\otimes_{\mathrm{Cu}}\mathrm{Cu}(B)$ for certain classes of $C^*$-algebras.

As a main tool for their approach the authors introduce the category $\mathrm{W}$ of pre-completed Cuntz semigroups. They show that $\mathrm{Cu}$ is a full, reflective subcategory of $\mathrm{W}$. One can then easily deduce properties of $\mathrm{Cu}$ from respective properties of $\mathrm{W}$, for example the existence of tensor products and inductive limits. The advantage is that constructions in $\mathrm{W}$ are much easier since the objects are purely algebraic.

Über diesen Titel

Über die Autorin bzw. den Autor

Ramon Antoine, Universitat Autonoma de Barcelona, Spain.

Francesc Perera, Universitat Autonoma de Barcelona, Spain.

Hannes Thiel, Universitat Munster, Germany.

Details zur Ausgabe

• Verlag: American Mathematical Society
• Erscheinungsdatum: 2018
• Sprache: Englisch
• ISBN 10: 1470427974
• ISBN 13: 9781470427979
• Einband: Tapa blanda
• Anzahl der Seiten: 191
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar