An algebra dense in its tidle algebra

We construct a closed setE in the circle such thatA(E) is dense, in but not equal to, its tilde algebra.     

Cyclic cohomology and algebra extensions

We construct a spectral sequence to study cyclic cohomology for an extension A = R/I of algebras. When R is a free algebra we describe the cyclic cohomology of A in terms of traces defined on R or powers of I. Explicit cyclic cocycles representing the cyclic cohomology class belonging to the trace are constructed as analogues of Chern character and Chern-Simons forms.Dedicated to Alexander Grothendieck     

Metrics with finite sets of primitive extensions

In this paper, we give a complete characterization for the class of rational finite metrics with the property that the set () of primitive extensions of is finite. Here, for a metric on a setT, a positive extensionm of to a setV T is calledprimitive if none of the convex combinations of other extensions of toV is less than or equal tom. Our main theorem asserts that the following the properties are equivalent: (i) () is finite; (ii) Up to an integer factor, is a submetric of the path metric d ^H of a graphH with |(d ^H )=1; (iii) A certain bipartite graph associated with contains neither isometrick-cycles withk6 nor induced subgraphsK _3,3 ^– . We then show that () is finite if and only if the dimension of the tight span of is at most two. We also present other results, discuss applications to multicommodity flows, and raise open problems.This research was supported by grant 97-01-00115 from the Russian Foundation of Basic Research and a grant from the Sonderforschungsbereich 343, Bielefeld Universität, Bielefeld, Germany.     

Prime top extensions of division algebra

Every division algebra of degreep ^t has a prime-to-p extension which is a crossed product, ifft ≤ 2. Research of the first author supported in part by the NSA/MSP Grant MDA90-H4001 while the author was on Sabbatical at Yale University Second author is grateful for support order NSF grant DMS-8901778     

Test sets for morphisms with bounded delay

Let p be a fixed nonnegative integer. We prove the Ehrenfeucht Conjecture for morphisms having deciphering delay bounded by p. In other words, we show that for each language L over a finite alphabet there exists a finite subset F of L such that for arbitrary morphisms h and g having deciphering delay bounded by p, the equation h(x) = g(x) holds for all x in L if and only if it holds for all x in F.     

Topologically transitive extensions of bounded operators

Let X be any Banach space and T a bounded operator on X. An extension of the pair (X,T) consists of a Banach space in which X embeds isometrically through an isometry i and a bounded operator on such that When X is separable, it is additionally required that be separable. We say that is a topologically transitive extension of (X, T) when is topologically transitive on , i.e. for every pair of non-empty open subsets of there exists an integer n such that is non-empty. We show that any such pair (X,T) admits a topologically transitive extension , and that when H is a Hilbert space, (H,T) admits a topologically transitive extension where is also a Hilbert space. We show that these extensions are indeed chaotic.Mathematics Subject Classification (2000): 47 A 16     

Families of sets with locally bounded width

A family of sets ? islocally k- wide if and only if the width (as a poset ordered by inclusion) of ? is at mostk for everyx. The directed covering graph of a locally 1-wide family of sets is a forest of rooted trees. It is shown that if ? is a locallyk-wide family of subsets of {1,...,n}, then |?|≤(2k) ^k?1 n. The proof involves a counting argument based on families of closed sets associated with theSperner closures in the filters of ?. The Sperner closure ofU in ? is the intersection of the members of the greatest Sperner antichain of ? _U = {V ∈ ?|V ?U}. This closure operation is related to a generalization of maximality in posets.     

Affine complete double Stone algebras with bounded core

Algebra universalis -     

The algebra of bounded holomorphic martingales

The algebra of bounded holomorphic martingales introduced by N. Th. Varopoulos (J. Funct. Anal., in press) is studied. In particular, it is shown that this is a logmodular algebra with a spectrum having no analytic structure.     

Retract extensions of ordered sets

The concept of retract extension of an ordered set is introduced and studied. We give an example of a retract extension and an example that is not a retract extension. Bibliography: 12 titles. Published in Zapiski Nauchnykh Seminarov POMI, Vol. 321, 2005, pp. 205–212.     

Sumsets of dense sets and sparse sets

R. Jin showed that whenever A and B are sets of integers having positive upper Banach density, the sumset A+B:= «a+b: a ∈ A, b ∈ B» is piecewise syndetic. This result was strengthened by Bergelson, Furstenberg, and Weiss to conclude that A+B must be piecewise Bohr. We generalize the latter result to cases where A has Banach density 0, giving a new proof of the previous results in the process.     

Constructing bounded remainder sets and cut-and-project sets which are bounded distance to lattices

For any irrational cut-and-project setup, we demonstrate a natural infinite family of windows which gives rise to separated nets that are each bounded distance to a lattice. Our proof provides a new construction, using a sufficient condition of Rauzy, of an infinite family of non-trivial bounded remainder sets for any totally irrational toral rotation in any dimension.     

Classification of extensions of torus algebra II

We use extension theory and algebraic methods to give a complete characterization of extensions of torus algebra by stable Cuntz algebras,and prove certain classification theorems of these extension algebras.     

Derivations and extensions of lie color algebra

In this article,the authors obtain some results concerning derivations of finitely generated Lie color algebras and discuss the relation between skew derivation space SkDer（L）and central extension H^2（L,F）on some Lie color algebras.Meanwhile,they generalize the notion of double extension to quadratic Lie color algebras,a sufficient condition for a quadratic Lie color algebra to be a double extension and further properties are given.