Related papers: Continuous trace C*-algebras, gauge groups and rat…

We classify spectrum-preserving endomorphisms of stable continuous-trace C^*-algebras up to inner automorphism by a surjective multiplicative invariant taking values in finite dimensional vector bundles over the spectrum. Specializing to…

We introduce an extended setting to study Hecke pairs $(G,H)$ which admit a regular representation on $L^2(H\backslash G)$, and consequently a $C^*$-algebra. As the result, many pairs of locally compact groups which had been studied in…

The concrete monotone $C^*$-algebra, that is the (unital) $C^*$-algebra generated by monotone independent algebraic random variables of Bernoulli type, is characterized abstractly in terms of generators and relations and is shown to be UHF.…

We construct a cohomology theory with compact support H^i_c(X_ar,Z(n))$ for separated schemes of finite type over a finite field, which should play a role analog to Lichtenbaum's Weil-etale cohomology groups for smooth and projective…

Let $G$ be a group scheme of finite type over a field, and consider the cohomology ring $H^*(G)$ with coefficients in the structure sheaf. We show that $H^*(G)$ is a free module of finite rank over its component of degree 0, and is the…

Let X be a compact Hausdorff space and let H be a separable Hilbert space. We prove that the group of all order automorphisms of the $C^*$-algebra $C(X)\otimes B(H)$ is algebraically reflexive.

In this paper we consider certain proejctions in the corona algebra of $C(X)\otimes B$ associated to $(p_0, p_1, \dots, p_n)$ where $p_i: X_i \to \mt_s$ a continuous projection valued section to the multiplier algebra of a stable…

We prove that all eight KO groups for a real C*-algebra can be constructed from homotopy classes of unitary matrices that respect a variety of symmetries. In this manifestation of the KO groups, all eight boundary maps in the 24-term exact…

Representations of $C^*$-algebras are realized on section spaces of holomorphic homogeneous vector bundles. The corresponding section spaces are investigated by means of a new notion of reproducing kernel, suitable for dealing with…

We prove gauge-invariant uniqueness theorems with respect to maximal and normal coactions for $C^*$-algebras associated to product systems of $C^*$-correspondences. Our techniques of proof are developed in the abstract context of Fell…

A gauge group is the topological group of automorphisms of a principal bundle. We compute the integral cohomology ring of the classifying spaces of gauge groups of principal U(n)-bundles over the 2-sphere by generalizing the operation for…

We calculate the rational cohomology of the commuting variety $X_{G, n}$ consisting of $n$-tuples of commuting elements of a compact reductive group $G$. This is done by studying a map from a related variety $Y_{G, n}$, which has easily…

Let $P$ be a submonoid of a group $G$ and let $\mathcal{E}=(\mathcal{E}_p)_{p\in P}$ be a product system over $P$ with coefficient C*-algebra $A$. We show that the following C*-algebras are canonically isomorphic: the C*-envelope of the…

Let $G$ be a real reductive Lie group, and $H^{\mathbb{C}}$ the complexification of its maximal compact subgroup $H\subset G$. We consider classes of semistable $G$-Higgs bundles over a Riemann surface $X$ of genus $g\geq2$ whose underlying…

We extend in this paper several results of E. Kirchberg, S. Wassermann and the author dealing with continuous fields of C*--algebras to the semi-continuous case. We provide a new characterisation of separable lower semi-continuity…

In this paper, we introduce a new class of structured spaces which is locally modeled by Costello's L-infinity spaces. This provides an alternative approach to study the derived geometric structures in the algebraic, analytic, or smooth…

Given a locally compact group bundle, we show that the system of the Plancherel weights of their C*-algebras is lower semi-continuous. As a corollary, we obtain that the dual Haar sytem of a continuous Haar system of a locally compact…

We classify certain algebras of matrix-valued cross-sections over an annulus up to complete isometric isomorphism, based on topological bundle invariants. In particular, we study sections of matrix bundles which are continuous on the…

We prove that strongly homotopy algebras (such as $A_\infty$, $C_\infty$, sh Lie, $B_\infty$, $G_\infty$,...) are homotopically invariant in the category of chain complexes. An important consequence is a rigorous proof that `strongly…

Suppose that A is a C*-algebra for which A is isomorphic to A tensor Z, where Z is the Jiang-Su algebra: a unital, simple, stably finite, separable, nuclear, infinite dimensional C*-algebra with the same Elliott invariant as the complex…