On the universal property of Pimsner-Toeplitz C*-algebras and their continuous analogues

We consider C*-algebras generated by a single Hilbert bimodule (Pimsner-Toeplitz algebras) and by a product systems of Hilbert bimodules. We give a new proof of a theorem of Pimsner, which states that any representation of the generating bimodule gives rise to a representation of the Pimsner-Toeplitz algebra. Our proof does not make use of the conditional expectation onto the subalgebra invariant under the dual action of the circle group. We then prove the analogous statement for the case of product systems, generalizing a theorem of Arveson from the case of product systems of Hilbert spaces.Comment: 10 page

Endomorphisms of Stable Continuous-Trace C^*-algebras

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 automorphisms, this gives a different approach to results of Phillips and Raeburn.Comment: 11 Page

Essential representations of C*-correspondences

Let E be a C*-correspondence over a C*-algebra \A with non-degenerate faithful left action. We show that E admits sufficiently many essential representations (i.e. representations \psi such that \psi(E)H = H to recover the Cuntz-Pimsner algebra O_E.Comment: 9 page

C*-algebras of Hilbert module product systems

We consider a class of C*-algebras associated to one parameter continuous tensor product systems of Hilbert modules, which can be viewed as continuous counterparts of Pimsner's Toeplitz algebras. By exhibiting a homotopy of quasihomomorphisms, we prove that those algebras are $K$-contractible. One special case is closely related to the Rieffel-Wiener-Hopf extension of a crossed product by R considered by Rieffel and by Pimsner and Voiculescu, and can be used to produce a new proof of Connes' analogue of the Thom isomorphism and in particular of Bott periodicity. Another special case is closely related to Arveson's spectral C*-algebras, and is used to settle Arveson's problem of computing their K-theory, extending earlier results of Zacharias to cover the general case.Comment: 11 pages (added an example and an appendix, corrected typos and improved exposition

On C∗C^*-algebras Associated to Certain Endomorphisms of Discrete Groups

Let \alpha:G --> G be an endomorphism of a discrete amenable group such that [G:\alpha(G)]<infinity. We study the structure of the C^* algebra generated by the left convolution operators acting on the left regular representation space, along with the isometry of the space induced by the endomorphism.Comment: 11 page

Rokhlin actions and self-absorbing C*-algebras

Let A be a unital separable C*-algebra, and D a K_1-injective strongly self-absorbing C*-algebra. We show that if A is D-absorbing, then the crossed product of A by a compact second countable group or by Z or by R is D-absorbing as well, assuming the action satisfying a Rokhlin property. In the case of a compact Rokhlin action we prove a similar statement about approximate divisibility.Comment: 15 pages; new coauthor joined; substantially revised and enlarged. Earlier results on a single automorphism were generalized, the case of finite groups was generalized to compact groups, and and a new section on Rokhlin flows was adde

Tracially Z-absorbing C*-algebras

We study a tracial notion of Z-absorption for simple, unital C*-algebras. We show that if A is a C*-algebra for which this property holds then A has almost unperforated Cuntz semigroup, and if in addition A is nuclear and separable we show this property is equivalent to having A being Z-absorbing. We furthermore show that this property is preserved under forming certain crossed products by actions satisfying a tracial Rokhlin type property.Comment: 17 pages. Minor revisions, to appear J. Funct. Ana

The Calkin algebra is not countably homogeneous

We show that the Calkin algebra is not countably homogeneous, in the sense of continuous model theory. We furthermore show that the connected component of the unitary group of the Calkin algebra is not countably homogeneous.Comment: Minor corrections. To appear in Proc. AM

The nuclear dimension of C*-algebras associated to homeomorphisms

We show that if X is a finite dimensional locally compact Hausdorff space, then the crossed product of C_0(X) by any automorphism has finite nuclear dimension. This generalizes previous results, in which the automorphism was required to be free. As an application, we show that group C*-algebras of certain non-nilpotent groups have finite nuclear dimension.Comment: With an appendix by Gabor Szabo. 28 pages. Minor typos corrected. To appear, Adv. Math. arXiv admin note: text overlap with arXiv:1308.5418 by other author

The Rokhlin property for endomorphisms and strongly self-absorbing C*-algebras

In this paper we define a Rokhlin property for automorphisms of non-unital C*-algebras and for endomorphisms. We show that the crossed product of a C*-algebra by a Rokhlin automorphism preserves absorption of a strongly self-absorbing C*-algebra, and use this result to deduce that the same result holds for crossed products by endomorphisms in the sense of Stacey. This generalizes earlier results of the second named author and W. Winter.Comment: 7 pages, minor revisions. To appear, Illinois Journal of Mathematic