We introduce a notion of noncommutative Choquet simplex, or briefly an nc that generalizes the classical simplex. While every simplex is there are many more simplices. They arise naturally from C*-algebras and in dynamics. characterize simplices terms their geometry structural properties corresponding operator systems. There natural definition Bauer show compact convex set if only it affinely h...

In this paper we study the unitary equivalence between Hilbert modules over a locally C∗-algebra. Also, we prove a stabilization theorem for countably generated modules over an arbitrary locally C∗-algebra and show that a Hilbert module over a Fréchet locally C∗-algebra is countably generated if and only if the locally C∗-algebra of all ”compact” operators has an approximate unit. 2000 Mathemat...

We prove the existence of a strict deformation quantization for the canonical Poisson structure on the dual of an integrable Lie algebroid. It follows that any Lie groupoid C-algebra may be regarded as a result of a quantization procedure. The C-algebra of the tangent groupoid of a given Lie groupoid G (with Lie algebra G) is the C-algebra of a continuous field of C-algebras over R with fibers ...

We define the concept of a partial translation structure T on a metric space X and we show that there is a natural C *-algebra C * (T) associated with it which is a subalgebra of the uniform Roe algebra C * u (X). We introduce a coarse invariant of the metric which provides an obstruction to embedding the space in a group. When the space is sufficiently group-like, as determined by our invarian...

A C∞-Hopf algebra is a C∞-algebra which is also a convenient Hopf algebra with respect to the structure induced by the evaluations of smooth functions. We characterize those C∞-Hopf algebras which are given by the algebra C∞(G) of smooth functions on some compact Lie group G, thus obtaining an anti-isomorphism of the category of compact Lie groups with a subcategory of convenient Hopf algebras.

A new C*-enlargement of a C*-algebra A nested between the local multiplier algebra Mloc(A) of A and its injective envelope I(A) is introduced. Various aspects of this maximal C*-algebra of quotients, Qmax(A), are studied, notably in the setting of AW*algebras. As a by-product we obtain a new example of a type I C*-algebra A such that Mloc(Mloc(A)) 6= Mloc(A).

We study the ideal structure of C∗-algebras arising from C∗-correspondences. We prove that gauge-invariant ideals of our C∗-algebras are parameterized by certain pairs of ideals of original C∗-algebras. We show that our C∗-algebras have a nice property which should be possessed by generalization of crossed products. Applications to crossed products by Hilbert C∗-bimodules and relative Cuntz-Pim...

To a directed graph E is associated a C∗-algebra C∗(E) called a graph C∗algebra. There is a canonical action γ of T on C∗(E), called the gauge action. In this paper we present necessary and sufficient conditions for the fixed point algebra C(E) to be simple. Our results also yield some structure theorems for simple graph algebras.

We study the ideal structure of C∗-algebras arising from C∗-correspondences. We prove that gauge-invariant ideals of our C∗-algebras are parameterized by certain pairs of ideals of original C∗-algebras. We show that our C∗-algebras have a nice property which should be possessed by generalization of crossed products. Applications to crossed products by Hilbert C∗-bimodules and relative Cuntz-Pim...