Let T be a tilting object in a triangulated category which is equivalent to the bounded derived category of a finite-dimensional hereditary algebra. The text investigages the strong global dimension, in the sense of Ringel, of the opposite algebra A of the endomorphism algebra of T . This invariant is expressed in terms of the lengths of the sequences T0, . . . , Tl of tilting objects such that...

We study the notion of positive and negative complexity of pairs of objects in cluster categories. The first main result shows that the maximal complexity occurring is either one, two or infinite, depending on the representation type of the underlying hereditary algebra. In the second result, we study the bounded derived category of a cluster tilted algebra, and show that the maximal complexity...

We define a tenlporal algebra that is applicable to any temporal relational data model supporting discrete linear bounded time. This algebra has the five basic relational algebra operators extended to the temporal domain and an operator of linear recursion. We show that this algebra has the expressive power of a safe temporal calculus based on the predicate temporal logic with the until and sin...

In this paper, we consider various extension problems associated with elements in the the closure with respect to either the multiplier norm or the completely bounded multiplier norm of the Fourier algebra of a locally compact group. In particular, we show that it is not always possible to extend an element in the closure with respect to the multiplier norm of the Fourier algebra of the free gr...

We prove that every module over a commutative homogeneous Koszul algebra has regularity bounded by its regularity over a polynomial ring of which the Koszul algebra is a homomorphic image. From this we derive a result conjectured by George Kempf to the effect that a suffkiently high truncation of any module over a homogeneous Koszul algebra has a linear free resolution. ‘E’ 1992 Academic Press....

We study embeddings of tracial $\mathrm{W}^*$-algebras into a ultraproduct matrix algebras through an amalgamation free probabilistic and model-theoretic techniques. Jung implicitly Hayes explicitly defined \emph{$1$-bounded entropy} the asymptotic covering numbers Voiculescu's microstate spaces, that is, spaces tuples $(X_1^{(N)},X_2^{(N)},\dots)$ having approximately same $*$-moments as gener...

In this article we review first some of the possibilities in which the notions of Følner sequences and quasidiagonality have been applied to spectral approximation problems. We construct then a canonical Følner sequence for the crossed product of a concrete C∗-algebra and a discrete amenable group. We apply our results to the rotation algebra (which contains interesting operators like almost Ma...

Let A be a unital complex Banach algebra. A linear mapping T : E → B from a subspace E ⊆ A into another unital complex Banach algebra B is called spectrally bounded if there is a constant M ≥ 0 such that r(Tx) ≤ Mr(x) for all x ∈ E. Here, and in what follows, r(x) stands for the spectral radius of a Banach algebra element x. This concept evolved in Banach algebra theory, and especially automati...

A Banach algebra A is weakly amenable provided that every bounded derivation from A to its dual A is inner. In H1], the rst-named author, building on earlier work of J. W. Bunce and W. L. Paschke BP], proved that every C-algebra is weakly amenable. We give a simpliied and uniied proof of this theorem. B. E. Johnson has proved that every bounded Jordan derivation from a C-algebra A to any Banach...

If G is a locally compact group, then the measure algebra M(G) and the completely bounded multipliers of the Fourier algebra McbA(G) can be seen to be dual objects to one another in a sense which generalises Pontryagin duality for abelian groups. We explore this duality in terms of representations of these algebras in spaces of completely bounded maps. This article is intended to give a tour of...