Tensor products and regularity properties of Cuntz semigroups. Memoirs of the American Mathematical Society; Bd. volume 251, number 1199 (sixth of 6 numbers).

Antoine, Ramon; Perera, Francesc; Thiel, Hannes

ISBN 10: 1470427974 / ISBN 13: 9781470427979

Published by Providence, American Mathematical Society, 2018

About this Item

Ex-library with stamp and library-signature. GOOD condition, some traces of use. C-03290 9781470427979 Sprache: Englisch Gewicht in Gramm: 550.

Seller Inventory # 2489195

Bibliographic Details

• Title: Tensor products and regularity properties of Cuntz semigroups. Memoirs of the American Mathematical Society; Bd. volume 251, number 1199 (sixth of 6 numbers).
• Publisher: Providence, American Mathematical Society
• Publication Date: 2018
• Language: English
• ISBN 10: 1470427974
• ISBN 13: 9781470427979
• Binding: Softcover
• Condition: Gut
• Weight: 550 grams
• Seller catalogs:
  • SA MATHEMATIK

About this title

Synopsis

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 $mathrmCu(A)$ is an object in the category $mathrmCu$ 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 $mathrmCu$-semigroups. The authors establish the existence of tensor products in the category $mathrmCu$ and study the basic properties of this construction. They show that $mathrmCu$ is a symmetric, monoidal category and relate $mathrmCu(Aotimes B)$ with $mathrmCu(A)otimesmathrmCumathrmCu(B)$ for certain classes of $C*$-algebras. As a main tool for their approach the authors introduce the category $mathrmW$ of pre-completed Cuntz semigroups. They show that $mathrmCu$ is a full, reflective subcategory of $mathrmW$. One can then easily deduce properties of $mathrmCu$ from respective properties of $mathrmW$, for example the existence of tensor products and inductive limits. The advantage is that constructions in $mathrmW$ are much easier since the objects are purely algebraic.

About the Author

Ramon Antoine, Universitat Autonoma de Barcelona, Spain.Francesc Perera, Universitat Autonoma de Barcelona, Spain.Hannes Thiel, Universitat Munster, Germany.