A relation between the anticyclic structure of the dendriform operad and the Coxeter transformations in the Grothendieck groups of the derived categories of modules over the Tamari posets is obtained.

First we construct spreads consisting of analytic curves (circular arcs and segments), without points of finite multiplicity. Then we see that, in the sense of Baire categories, most such spreads have no points of finite multiplicity.

Amenable actions of locally compact groups on von Neumann algebras are investigated by exploiting the natural module structure of the crossed product over the Fourier algebra of the acting group. The resulting characterization of injectivity for crossed products generalizes a result of Anantharaman-Delaroche on discrete groups. Amenable actions of locally compact groups on $C^*$ -algebras are investigated in the same way, and amenability of the action is related to nuclearity of the corresponding crossed product. A survey is given to show that this notion of amenable action for $C^*$ -algebras satisfies a number of expected properties. A notion of inner amenability for actions of locally compact groups is introduced, and a number of applications are given in the form of averaging arguments, relating approximation properties of crossed product von Neumann algebras to properties of the components of the underlying $w^*$ -dynamical system. We use these results to answer a recent question of Buss, Echterhoff, and Willett.

Let (P, ≥) be a p.o. set. The basis graph of (P, ≥) is defined to be the directed graph whose vertex set is P and in which the ordered pair 〈a, b〉 is an edge if and only if b covers a in (P, ≥).

Let D be a directed graph. All graphs considered in this note are finite and are free of loops and multiple edges.

This paper contains a geometric proof of an estimate for a restricted x-ray transform. The result complements one of A. Greenleaf and A. Seeger.

An application of graph theory to automatic traffic control [2] gave rise to the problem of deciding which connected graphs have points of degree 2 which can be successively suppressed until only a single edge remains.

Denote by g(n) the largest integer m such that every set of integers of size n contains a subset of size m whose pairwise sums are distinct. It is shown that g(n) > cn1/2 for any constant c < 2/25 and all sufficiently large n.

We prove an algebraic “no-go theorem” to the effect that a nontrivial Poisson algebra cannot be realized as an associative algebra with the commutator bracket. Using it, we show that there is an obstruction to quantizing the Poisson algebra of polynomials generated by a nilpotent basic algebra on a symplectic manifold. This result generalizes Groenewold’s famous theorem on the impossibility of quantizing the Poisson algebra of polynomials on ${{\mathbf{R}}^{2n}}$. Finally, we explicitly construct a polynomial quantization of a symplectic manifold with a solvable basic algebra, thereby showing that the obstruction in the nilpotent case does not extend to the solvable case.

Let $f(x)=x^{6}+ax^{4}+bx^{2}+c$ be an irreducible sextic polynomial with coefficients from a field $F$ of characteristic $\neq 2$, and let $g(x)=x^{3}+ax^{2}+bx+c$. We show how to identify the conjugacy class in $S_{6}$ of the Galois group of $f$ over $F$ using only the discriminants of $f$ and $g$ and the reducibility of a related sextic polynomial. We demonstrate that our method is useful for producing one-parameter families of even sextic polynomials with a specified Galois group.

For each nonnegative integer r,

is represented by a multiple series which is expressed in terms of rational numbers and the special values of the zeta function Thus, the set serves as a kind of basis for expressing all of the values

The classical rings of number theory, Dedekind domains, are characterized by the property that every ideal is a product of prime ideals. More generally, a commutative ring R with identity has the property that every ideal is a product of prime ideals if and only if R is a finite direct sum of Dedekind domains and special principal ideal rings. These rings, called general Z.P.I. rings, are also characterized by the property that every (prime) ideal is finitely generated and locally principal.

We give an elementary potential-theoretic proof of a theorem of G. Johnsson: all solutions of Cauchy’s problems for the Laplace equations with an entire data on a sphere extend harmonically to the whole space RN except, perhaps, for the center of the sphere.

Let $R\,=\,\oplus _{i=1}^{\infty }\,{{R}_{i}}$ be a graded nil ring. It is shown that primitive ideals in $R$ are homogeneous. Let $A\,=\,\oplus _{i=1}^{\infty }\,{{A}_{i}}$ be a graded non-PI just-infinite dimensional algebra and let $I$ be a prime ideal in $A$. It is shown that either $I\,=\,\{0\}$ or $I\,=\,A$. Moreover, $A$ is either primitive or Jacobson radical.

We carry out the computation of the Iwasawa invariants $\rho _{S}^{T},\,\mu _{S}^{T},\,\lambda _{S}^{T}$ associated to abelian $T$-ramified $S$-decomposed $\ell$-extensions over the finite steps ${{K}_{n}}$ of the cyclotomic ${{\mathbb{Z}}_{\ell }}$ -extension ${{K}_{\infty }}/K$ of a number field of CM-type.

We study the pure infiniteness of C* -crossed products by endomorphisms and automorphisms. Let A be a purely infinité simple unital C*-algebra. At first we show that a crossed product A × p N by a corner endomorphism p is purely infinite if it is simple. From this observation we prove that any simple C*-crossed products A ×αZ by an automorphism α is purely infinite. Combining this with the result in [Je] on pure infiniteness of crossed products by finite groups, one sees that if α is an outer action by a countable abelian group G then the simple C*-algebra A ×α G is purely infinite.

We give characterizations of Toeplitz operators on generalised H2 spaces and derive some properties of the corresponding Toeplitz algebras. The proofs depend essentially on having a "sufficient" supply of inner functions.

In this note we present inequalities relating the successive minima of an $o$-symmetric convex body and the successive inner and outer radii of the body. These inequalities join known inequalities involving only either the successive minima or the successive radii.

We study natural $*$-valuations, $*$-places and graded $*$-rings associated with $*$-ordered rings. We prove that the natural $*$-valuation is always quasi-Ore and is even quasi-commutative (i.e., the corresponding graded $*$-ring is commutative), provided the ring contains an imaginary unit. Furthermore, it is proved that the graded $*$-ring is isomorphic to a twisted semigroup algebra. Our results are applied to answer a question of Cimprič regarding $*$-orderability of quantum groups.

It is a question of Arhangel'skiĭ [1] (Problem 2) whether the identity ψ(G) = X(G) holds for every minimal Hausdorff topological group G = 〈G,u〉). (Here, as usual, ψ(G), the pseudocharacter of G, is the least cardinal number K for which there is such that and and x(G), the character of G,is the least cardinality of a local base at e for (〈G,u〉.) That 〈G, u〉 is minimal means that, if v is a Hausdorff topological group topology for G and v ⊂ u, then v = u.

In this paper, we give some conditions on G sufficient to ensure a positive response to Arhangel'skiï's question, and we offer an example which responds negatively to a question on minimal groups posed some years ago (cf. [6] (p. 107) and [4] (p. 259)).

In his recent book [3] Nadler observes that the property of admitting a Whitney map is of fundamental importance in studying the internal structure of hyperspaces, especially their arc structure. Nadler presents three distinct methods of constructing a Whitney map on the hyperspace 2X of nonempty closed subsets of a continuum.

A partially ordered space is a topological space X endowed with a partial order ≤ whose graph is a closed subset of X×X. It is well-known (see, for example, [2], page 167) that if X is a regular Hausdorff space then 2X is a partially ordered space with respect to inclusion.