Tensor Products and Regularity Properties of Cuntz Semigroups Paperback / softback
by Ramon Antoine, Francesc Perera, Hannes Thiel
Part of the Memoirs of the American Mathematical Society series
Paperback / softback
Description
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.
Information
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Available to Order - This title is available to order, with delivery expected within 2 weeks
- Format:Paperback / softback
- Pages:191 pages
- Publisher:American Mathematical Society
- Publication Date:30/03/2018
- Category:
- ISBN:9781470427979
Other Formats
- PDF from £70.20
Information
-
Available to Order - This title is available to order, with delivery expected within 2 weeks
- Format:Paperback / softback
- Pages:191 pages
- Publisher:American Mathematical Society
- Publication Date:30/03/2018
- Category:
- ISBN:9781470427979
