Related papers: Relative $K$-theory for $C^*$-algebras

We show that semigroup C*-algebras attached to ax+b-semigroups over rings of integers determine number fields up to arithmetic equivalence, under the assumption that the number fields have the same number of roots of unity. For finite…

Goodwillie's rational isomorphism between relative algebraic K-theory and relative cyclic homology, together with the lambda decomposition of cyclic homology, illustrates the close relationships among algebraic K-theory, cyclic homology,…

We use a recent result by Cuntz, Echterhoff and Li about the K-theory of certain reduced C*-crossed products to describe the K-theory of C*_r(S) when S is an inverse semigroup satisfying certain requirements. A result of Milan and Steinberg…

Let $A$ and $B$ be separable $C^*$-algebras, $A$ unital and $B$ stable. It is shown that there is a natural six-terms exact sequence which relates the group which arises by considering all semi-split extensions of $A$ by $B$ to the group…

This work is intended to present the basic properties of $KO$-theory for real $C^*$-algebras and to explain its relationship with complex $K$-theory and with $KR$- theory. Whenever possible we will rely upon proofs in printed literature,…

We describe Markov interval maps via branching systems and develop the theory of relative branching systems, characterizing when the associated representations of relative graph C*-algebras are faithful. When the Markov interval maps $f$…

These notes are based on a lecture course given by the first author in the Sedano Winter School on K-theory held in Sedano, Spain, on January 22-27th of 2007. They aim at introducing K-theory of C^*-algebras, equivariant K-homology and…

This is the first of two papers dedicated to the computation of the reduced C*-algebra of a connected, linear, real reductive group up to Morita equivalence, and the verification of the Connes-Kasparov conjecture for these groups. These…

In this paper we show that for an almost finite minimal ample groupoid $G$, its reduced $\mathrm{C}^*$-algebra $C_r^*(G)$ has real rank zero and strict comparison even though $C_r^*(G)$ may not be nuclear in general. Moreover, if we further…

It is shown that if $A$ and $B$ are unital separable simple nuclear $\mathcal Z$-stable C$^*$-algebras and there is a unital embedding $A \rightarrow B$ which is invertible on $KK$-theory and traces, then $A \cong B$. In particular, two…

In this paper we construct and study the representation theory of a Hopf C^*-algebra with approximate unit, which constitutes quantum analogue of a compact group C^*-algebra. The construction is done by first introducing a…

Following a result of Hatori, Miura and Tagaki ([4]) we give here a spectral characterization of an isomorphism from a $C^\star$-algebra onto a Banach algebra. We then use this result to show that a $C^\star$-algebra $A$ is isomorphic to a…

Under suitable conditions, a substitution tiling gives rise to a Smale space, from which three equivalence relations can be constructed, namely the stable, unstable, and asymptotic equivalence relations. We denote with $S$, $U$, and $A$…

Let A be a Banach algebra and I be a closed ideal of A. We say that A is amenable relative to I, if A/I is an amenable Banach algebra. We study the relative amenability of Banach algebras and investigate the relative amenability of…

We introduce controlled $KK$-theory groups associated to a pair $(A,B)$ of separable $C^*$-algebras. Roughly, these consist of elements of the usual $K$-theory group $K_0(B)$ that approximately commute with elements of $A$. Our main results…

We prove the $K$-theoretic Farrell-Jones conjecture for groups as in the title with coefficient rings and $C^*$-algebras which are stable with respect to compact operators. We use this and Higson-Kasparov's result that the Baum-Connes…

We show that every strongly $\mathbb{Z}$-graded C*-algebra (equivalently, every C*-algebra carrying a strongly continuous $\mathbb{T}$-action with full spectral subspaces) is a Cuntz--Pimsner algebra, and describe subalgebras and subspaces…

Non-commutative $L^p$-spaces are shown to constitute examples of a class of Banach quasi *-algebras called CQ*-algebras. For $p\geq 2$ they are also proved to possess a {\em sufficient} family of bounded positive sesquilinear forms…

We compute the genus of a rational quadratic form in terms of the K-theory of a C*-algebra attached to the adelic orthogonal group of the form. As a corollary, one gets a higher composition law for the rational quadratic forms. As an…

In this paper we identify many striking elements in Leibniz (co)homology which arise from characteristic classes and K-theory. For a group G a field k of characteristic zero, it is shown that all primary characteristic classes, i.e. H^*(BG;…