Given a cluster-tilted algebra B we study its first Hochschild cohomology group HH(B) with coefficients in the B–B-bimodule B. If C is a tilted algebra such that B is the relation extension of C by E = ExtC(DC,C), then we prove that HH (B) is isomorphic, as a vector space, to the direct sum of HH(C) with HH(B,E). This yields homological interpretations for results of the first and the fourth au...

Let A be a Banach algebra, and let E be a Banach A-bimodule. A linear map S :AMNE is intertwining if the bilinear map (a, b)PN (δ"S ) (a, b)B a[Sb®S(ab)­Sa[b, A¬AMNE, is continuous, and a linear map D :AMNE is a deriŠation if δ"D ̄ 0, so that a derivation is an intertwining map. Derivations from A to E are not necessarily continuous. The purpose of the present paper is to prove that the continui...

To a B-coring and a (B, A)-bimodule that is finitely generated and projective as a right A-module an A-coring is associated. This new coring is termed a base ring extension of a coring by a module. We study how the properties of a bimodule such as separability and the Frobenius properties are reflected in the induced base ring extension coring. Any bimodule that is finitely generated and projec...

In this article, we will give a characterization of Banach bimodules over C∗-algebras of compact operators that arises from operator spaces as well as a characterization of (F)-Banach bundles amongst all (H)-Banach bundles over a hyper-Stonian space. These two characterizations are concerned with whether certain natural map from a Banach bimodule to its canonical bidual is isometric (we call su...

We show that if E is an equivalence of upper semicontinuous Fell bundles B and C over groupoids, then there is a linking bundle L(E ) over the linking groupoid L such that the full cross-sectional algebra of L(E ) contains those of B and C as complementary full corners, and likewise for reduced cross-sectional algebras. We show how our results generalise to groupoid crossed-products the fact, p...

With every (strict or normal) unital endomorphism of the algebra of all adjointable operators on a Hilbert module there is associated a correspondence (that is, a Hilbert bimodule) such that the endomorphism can be recovered as amplification of the identity representation with that correspondence. In these notes we show the converse of this statement in the case of strongly full W–correspondenc...

Let (M,N ) be a pair of von Neumann algebras, or of dual operator spaces with at least one of them having property Sσ, and let Φ be an arbitrary completely bounded mapping on M. We present an explicit construction of an amplification of Φ to a completely bounded mapping on M⊗N . Our approach is based on the concept of slice maps as introduced by Tomiyama, and makes use of the description of the...

We consider the problem of classifying all finite basis-transitive matroids and reduce it to the classification of the finite basis-transitive and point-primitive simple matroids (or geometric lattices, or dimensional linear spaces). Our main result shows how a basisand point-transitive simple matroid is decomposed into a so-called supersum. In particular each block of imprimitivity bears the s...