Strong perforation in infinitely generated K_0-groups of simple C*-algebras

Perforation conditions and almost algebraic order in Cuntz semigroups

For a C$^*$-algebra $A$, it is an important problem to determine the Cuntz semigroup $\mathrm{Cu}(A\otimes\mathcal{Z})$ in terms of $\mathrm{Cu}(A)$. We approach this problem from the point of view of semigroup tensor products in the category of abstract Cuntz semigroups, by analysing the passage of significant properties from $\mathrm{Cu}(A)$ to $\mathrm{Cu}(A)\otimes_\mathrm{Cu}\mathrm{Cu}(\mathcal{Z})$. We describe the effect of the natural map $\mathrm{Cu}(A)\to\mathrm{Cu}(A)\otimes_\mathrm{Cu}\mathrm{Cu}(\mathcal{Z})$ in the order of $\mathrm{Cu}(A)$, and show that, if $A$ has real rank z…

Compact endomorphisms of Banach algebras of infinitely differentiable functions

We consider non-zero endomorphisms of the Dales and Davie algebras of infinitely differentiable functions on intervals in the real line. We discuss necessary and sufficient conditions for a selfmap of the interval to induce a compact endomorphism of these algebras. We also determine the spectra of these compact endomorphisms.

无私 C*-代数

Selfless C*-algebras

本文提出并介绍了一类称为“无私 C*-代数”的单 C*-代数，涵盖 Jiang-Su 代数、无限维 UHF 代数、自由群约化群 C*-代数及 Cuntz 代数等重要例子。

Infinitely many star products to play with

While there has been growing interest for noncommutative spaces in recent times, most examples have been based on the simplest noncommutative algebra: [x_i,x_j]=i theta_{ij}. Here we present new classes of (non-formal) deformed products associated to linear Lie algebras of the kind [x_i,x_j]=ic_{ij}^k x_k. For all possible three-dimensional cases, we define a new star product and discuss its properties. To complete the analysis of these novel noncommutative spaces, we introduce noncompact spectral triples, and the concept of star triple, a specialization of the spectral triple to deformations …

K-homology of the CAR algebra

We compare the K-theory and K-homology of the well known CAR algebra. While the $K_0$ group is infinitely generated, we shows that it pairs identically to zero with even Fredholm modules over the algebra. We show further that in fact the even K-homology is trivial, while the odd K-homology is very large. These results give some insight into the K-homology of AF-algebras.

可分类的C*-代数具有量子对称性

Classifiable C*-algebras have quantum symmetries

本文证明可分类简单C*-代数（如Jiang-Su代数）具有离散量子群外作用，并由此构造新的超有限子因子及SU_q(2)的极小作用。