(B n * GnSn) — Geometrien

A consequence of BENZ [3], [4] and ARTZY [2] is that the class of all (B ₂ ^* S₂)-geometries coinzides with the class of the chain geometries (K,K×K), K a commutative field. Therefore the tangency theorem holds in every (B ₂ ^* S₂)-geometry.In this paper we present a corresponding tangency theorem for (B ₃ ^* G₃S₃)-geometries and prove that up to isomorphisms the (B _n ^* G_nS_n)-geometries, n>1, are exactly the chain geometries (K,Kⁿ).     

The structure of 0-bisimple strongly E *-unitary inverse monoids

We introduce a class of strongly E ^*-unitary inverse semigroups S _i (G, P) (i = 1,2) determined by a group G and a submonoid P of G and give an embedding theorem for S _i (G, P). Moreover we characterize 0-bisimple strongly E ^*-unitary inverse monoids and 0-bisimple strongly F ^*-inverse monoids by using S _i (G, P).     

Integrably asymptotic affine homeomorphisms of the circle and Teichmüller spaces

A quasisymmetric homeomorphism of the unit circle S¹ is called integrably asymptotic affine if it admits a quasiconformal extension into the unit disk so that its complex dilatation is square integrable in the Poincaré metric on the unit disk. Let QS_* (s¹) be the space of such maps. Here we give some characterizations and properties of maps in QS_* (S¹). We also show that QS_* (S₁)/M?b (S¹) is the completion of Diff(S¹)/M?b(S₁) in the Weil-Petersson metric.     

The Structure of 0 -Bisimple Strongly E * -unitary Inverse Monoids

Abstract. We introduce a class of strongly E ^* -unitary inverse semigroups S _i (G,P) (i=1,2) determined by a group G and a submonoid P of G and give an embedding theorem for S _i (G,P) . Moreover we characterize 0 -bisimple strongly E ^* -unitary inverse monoids and 0 -bisimple strongly F ^* -inverse monoids by using S _i (G,P) .     

A set of maps from K to EndA(l2(A)) isomorphic to EndA(K)(l2(A(K))). Applikations

Let A be a C^*-algebra, K be a compact space, A(K) be the C^*-algebra of all continuous maps from K into A, 1₂(A) be the standard countably generated Hilbert A-module. We investigate a set of maps from K into End_A(1₂(A)), which is isomorphic to End_A(K)(1₂(A(K))). We describe the subsets which are isomorphic to End_fA(K) ^*(1₂(A(K))). GL_A(K)(1₂(A(K))) and GL_fA(K) ^*(1₂(A(K))), respectively. As an application we deduce a criterion for the self-duality of 1₂(A) in the commutative case.     

Elementary divisors of induced transformations on symmetry classes of tensors

Let V_χ(G) denote the symmetry class of tensors over the vector space V associated with the permutation group G and irreducible character χ. Write v₁*v₂*...*v_m for the decomposable symmetrized product of the indicated vectors (m=degG). If T is a linear operator on V, let K(T) denote the associated operator on V_χ(G), i.e., K(T)v₁*v₂*...*v_m=Tv₁*Tv₂*...*Tv_m. Denote by D(T) the derivation operator D(T)v₁*v₂*...*v_m=Tv₁*v₂...*v_m+v₁*Tv₂*v₃* ...*v_m+...+v₁*v₂*...*v_m–1*Tv_m. The article concerns the elementary divisors of K(T) and D(T).     

A problem about the weak Hilbert property

In this paper, we prove the main result: Let both (K, S) and (K ^*,S ^*) be preordered fields, and let (K ^*,S ^*) be a finitely generated extension of (K, S). IfK ^* is transcendental overK, then (K ^*,S ^*) has the weak Hilbert property. This result answers negatively an open problem posed by the author in reference [1]. Moreover, some results on the weak Hilbert property are established. Project supported by National Natural Science Foundation of China     

On alternating and symmetric groups as Galois groups

Fix an integern≧3. We show that the alternating groupA _n appears as Galois group over any Hilbertian field of characteristic different from 2. In characteristic 2, we prove the same whenn is odd. We show that any quadratic extension of Hilbertian fields of characteristic different from 2 can be embedded in anS _n-extension (i.e. a Galois extension with the symmetric groupS _n as Galois group). Forn≠6, it will follow thatA _n has the so-called GAR-property over any field of characteristic different from 2. Finally, we show that any polynomialf=X ⁿ+…+a₁X+a₀ with coefficients in a Hilbertian fieldK whose characteristic doesn’t dividen(n-1) can be changed into anS _n-polynomialf ^* (i.e the Galois group off ^* overK Gal(f ^*, K), isS _n) by a suitable replacement of the last two coefficienta ₀ anda ₁. These results are all shown using the Newton polygon. The author acknowledges the financial support provided through the European Community’s Human Potential Programme under contract HPRN-CT-2000-00114, GTEM.     

On the decidability of the word problem for amalgamated free products of inverse semigroups

We study inverse semigroup amalgams [S ₁,S ₂;U], where S ₁ and S ₂ are finitely presented inverse semigroups with decidable word problem and U is an inverse semigroup with decidable membership problem in S ₁ and S ₂. We use a modified version of Bennett’s work on the structure of Schützenberger graphs of the ℛ-classes of S ₁* _U S ₂ to state sufficient conditions for the amalgamated free products S ₁* _U S ₂ having decidable word problem.     

Solvability of a convolution equation in convex domains

For an exponential functiona(z) we consider the convolutiona* x in the function space H(G), consisting of functions analytic in convex domains G. We obtain conditions (close to necessary and sufficient) on G and G₁ subject to which the equationa* (H(G₁)) = H(G) is satisfied.     

Large k-preserving sets in infinite graphs

Let K be a cardinal. If K χ₀, define K := K . Otherwise, let K := K + 1. We prove a conjecture of Mader: Every infinite K -connected graph G = (V, E) contains a set S ? V with |S| = |V| such that G/S is K -connected for all S? S.     

The GL2 Main Conjecture for Elliptic Curves without Complex Multiplication

Let G be a compact p-adic Lie group, with no element of order p, and having a closed normal subgroup H such that G/H is isomorphic to Z_p. We prove the existence of a canonical Ore set S^* of non-zero divisors in the Iwasawa algebra Λ(G) of G, which seems to be particularly relevant for arithmetic applications. Using localization with respect to S^*, we are able to define a characteristic element for every finitely generated Λ(G)-module M which has the property that the quotient of M by its p-primary submodule is finitely generated over the Iwasawa algebra of H. We discuss the evaluation of this characteristic element at Artin representations of G, and its relation to the G-Euler characteristics of the twists of M by such representations. Finally, we illustrate the arithmetic applications of these ideas by formulating a precise version of the main conjecture of Iwasawa theory for an elliptic curve E over Q, without complex multiplication, over the field F generated by the coordinates of all its p-power division points; here p is a prime at least 5 where E has good ordinary reduction, and G is the Galois group of F over Q.     

A non-nice extreme operator

We give examples of an Eberlein-compact spaceX such that, ifS _x is the unit ball ofC(X)* with thew*-topology then the operatorT: C(X)→C(S _x ) defined byTf(μ) = μ(f), f ∈(X), μ ∈ S _x , is a non-nice extreme operator.     

Topologically minimal surfaces versus self-amalgamated Heegaard surfaces

Let V ∪SW be a Heegaard splitting of M,such that αM = α-W = F1 ∪ F2 and g(S) = 2g(F1)= 2g(F2). Let V * ∪S*W * be the self-amalgamation of V ∪SW. We show if d(S) 3 then S* is not a topologically minimal surface.     

Noncommutative Chern Characters of Compact Lie Group C*-Algebras

For compact Lie groups, the Chern characters K^*(G) Q H^* _DR(G;Q) have been already constructed. In this paper, we construct and study the corresponding noncommutative Chern characters. They are homomorphisms ch_C*: K_*(C^*(G)) from quantum K-groups into entire current periodic cyclic homology groups of group C^*-algebras. We also obtain the corresponding algebraic version ch_alg: K_*(C^*(G)) HP_*(C^*(G)), which can be identified with the classical Chern character K_* (C(T)) HP_* (C(T)), where T is the maximal torus of G.     

Duality theorems for regular homotopy of finite directed graphs

Dati uno spazio topologico normale e numerabilmente paracompattoS ed un grafo finito ed orientatoG si prova che tra gli insiemiQ(S, G) eQ ^*(S, G) delle classi dio-omotopia e dio ^*-omotopia esiste una biiezione naturale. Nelle stesse condizioni, seS′ è un sottospazio chiuso diS eG′ un sottografo diG, esiste ancora una biiezione naturale tra gli insiemiQ (S, S′; G, G′) eQ ^* (S, S′; G, G′) delle classi di omotopia. Si mostra infine che in condizioni meno restrittive per lo spazioS le precedenti biiezioni possono non sussistere.     

The cross-ratio distortion of integrably asymptotic affine homeomorphism of unit circle

Let QS* (S 1) be the space of quasisymmetric homeomorphisms of the unit circle such that the corresponding subspace of the universal Teichmu¨ller space has Weil-Petersson metric.In this paper we give a necessary condition for a quasisymmetric homeomorphism to belong to QS *(S 1) from the aspect of cross-ratio distortion.     

Characterizations of finite groups by sets of orders of their elements

For a finite group G, ω(G) denotes the set of orders of its elements. If ω is a subset of the set of natural numbers, h(ω) stands for the number of pairwise nonisomorphic finite groups G for which ω(G)=ɛ. We prove that h(ω(G))=1, if G is isomorphic to S₉, S₁₁, S₁₂, S₁₃, or A₁₂, and h(ω(G))=2 if G is isomorphic to S₂(6) or to O ₈ ⁺ (2). 01 Supported by RFFR grant No. 96-01-01893. Translated fromAlgebra i Logika, Vol. 36, No. 1, pp. 37–53, January–February, 1997.