Related papers: Polar decomposition in algebraic K-theory

We classify the unital embeddings of a unital separable nuclear $C^*$-algebra satisfying the universal coefficient theorem into a unital simple separable nuclear $C^*$-algebra that tensorially absorbs the Jiang--Su algebra. This gives a new…

We present the first range result for the total K-theory of C*-algebras. This invariant has been used successfully to classify certain separable, nuclear C*-algebras of real rank zero. Our results complete the classification of the…

Using methods from coarse topology we show that fundamental classes of closed enlargeable manifolds map non-trivially both to the rational homology of their fundamental groups and to the K-theory of the corresponding reduced C*-algebras.…

We determine the class of finite T_0-spaces allowing for a universal coefficient theorem computing equivariant KK-theory by filtrated K-theory.

Let a compact group G act on real or complex C*-algebras A and B, with A separable and B sigma-unital. We express the G-equivariant Kasparov groups KK_n(A,B) by algebraic K-groups of a certain additive category.

We show that separable continuous fields over the unit interval whose fibers are stable Kirchberg algebras that satisfy the universal coefficient theorem in KK-theory and have rational K-theory groups are classified up to isomorphism by…

We prove that if a connected and simply connected Lie group $G$ admits connected closed normal subgroups $G_1\subseteq G_2\subseteq \cdots \subseteq G_m=G$ with $\dim G_j=j$ for $j=1,\dots,m$, then its group $C^*$-algebra has closed…

Let $K$ be a compact metric space and let $\varphi: K \to K$ be continuous. We study C*-algebra $\mathcal{MC}_\varphi$ generated by all multiplication operators by continuous functions on $K$ and a composition operator $C_\varphi$ induced…

Gelfand - Na\u{i}mark theorem supplies a one to one correspondence between commutative $C^*$-algebras and locally compact Hausdorff spaces. So any noncommutative $C^*$-algebra can be regarded as a generalization of a topological space.…

We compute the group homology, the topological K-theory of the reduced C^*-algebra, the algebraic K-theory and the algebraic L-theory of the group ring of the semi-direct product of the three-dimensional discrete Heisenberg group by Z/4.…

Let $\mathfrak{g}$ be a Lie algebra in characteristic zero equipped with a vector space decomposition $\mathfrak{g}=\mathfrak{g}^-\oplus \mathfrak{g}^+$, and let $s$ and $t$ be commuting formal variables. We prove that the…

A {\it separated graph} is a pair $(E,C)$ consisting of a directed graph $E$ and a set $C=\bigsqcup_{v\in E^0}C_v$, where each $C_v$ is a partition of the set of edges whose terminal vertex is $v$. Given a separated graph $(E,C)$, such that…

We solve the isomorphism problem for essential unital $C^*$-algebra extensions of the form $0 \to \mathcal{K} \oplus \mathcal{K} \to E \xrightarrow{\pi} M_n \otimes C(\mathbb{T}) \to 0$. We then relate these to analogs of the Effros Shen AF…

A generalization of Connes-Thom isomorphism is given for stable, homotopy invariant, and split exact functors on separable $C^*$-algebras. As examples of these functors, we concentrate on asymptotic and local cyclic cohomology and the…

An affine Hecke algebra H contains a large abelian subalgebra A. The center Z of H is the subalgebra of Weyl group invariant elements in A. The natural trace of the affine Hecke algebra can be written as an integral of a rational $n$ form…

Let $A \to B$ be a $G$-Galois extension of rings, or more generally of $\mathbb{E}_\infty$-ring spectra in the sense of Rognes. A basic question in algebraic $K$-theory asks how close the map $K(A) \to K(B)^{hG}$ is to being an equivalence,…

Nuclear $C^*$-algebras having a system of completely positive approximations formed with convex combinations of a uniformly bounded number of order zero summands are shown to be approximately finite dimensional.

This is a survey article describing the proof that the crossed product C^* (Z, M, h) of a compact smooth manifold M by a minimal diffeomorphism h of M is isomorphic to a direct limit of recursive subhomogeneous C*-algebras.

We use a unified method to give an isomorphism between direct sums of cyclotomic affine (and degenerate affine) Hecke algebras and cyclotomic BK-subalgebras which are some KLR-type algebras.

The first part of the paper is a brief overview of Hindman's finite sums theorem, its prehistory and a few of its further generalizations, and a modern technique used in proving these and similar results, which is based on idempotent…