Tensor Products and Regularity Properties of Cuntz Semigroups
Seiten
2018
American Mathematical Society (Verlag)
978-1-4704-2797-9 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-2797-9 (ISBN)
- Titel z.Zt. nicht lieferbar
- Versandkostenfrei
- Auch auf Rechnung
- Artikel merken
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.
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.
Ramon Antoine, Universitat Autonoma de Barcelona, Spain. Francesc Perera, Universitat Autonoma de Barcelona, Spain. Hannes Thiel, Universitat Munster, Germany.
Introduction
Pre-completed Cuntz semigroups
Completed Cuntz semigroups
Additional axioms
Structure of Cu-semigroups
Bimorphisms and tensor products
Cu-semirings and Cu-semimodules
Structure of Cu-semirings
Concluding remarks and Open Problems
Appendix A. Monoidal and enriched categories
Appendix B. Partially ordered monoids, groups and rings
Bibliography
Index of Terms
Index of Symbols
| Erscheinungsdatum | 07.01.2018 |
|---|---|
| Reihe/Serie | Memoirs of the American Mathematical Society |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 298 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 1-4704-2797-4 / 1470427974 |
| ISBN-13 | 978-1-4704-2797-9 / 9781470427979 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
| Haben Sie eine Frage zum Produkt? |
Mehr entdecken
aus dem Bereich
aus dem Bereich
Eine Einführung für Studienanfänger
Buch | Softcover (2025)
Springer Spektrum (Verlag)
CHF 41,95
Sieben ausgewählte Themenstellungen
Buch | Softcover (2024)
De Gruyter Oldenbourg (Verlag)
CHF 89,95
