Homogeneous algebraic varieties defined by Jordan pairs

Every Jordan pair defines an algebraic varietyX containing as a dense open subset.X is projective (affine) if and only if is separable (radical). The Picard group ofX is generated by the irreducible factors of the generic norm of . If is separable then the automorphism group ofX is the projective group of .     

Chu-Dualität und zwei Klassen maximal fastperiodischer Gruppen

This is a continuation of the paper Zwei Klassen lokalkompakter maximal fastperiodischer Gruppen, [6]. In [6], the classes and were introduced. We give sufficient conditions to conclude thatG is in if one knows thatG/G ₀ is in . If a groupG is in and ifG satisfies the Chu-duality then all closed subgroups ofG satisfy the Chu-duality. The Chu-quasi-dual of the Heisenberg groupH with integral coefficients is computed. It is shown thatH does not satisfy the Chu-duality, thatH is in , and thatH is not in .     

Functions of translation type and functorial properties of Segal algebras II

In this paper we investigate functorial properties of the Segal algebra which consists of all functionsf in Wiener's algebra onG with Fourier transform in Wiener's algebra on the dual group . Especially may serve as a very large and natural domain for Poisson's formula. Moreover, there is introduced a Segal algebraE ₀(G) containing as a subspace, but still eachfE ₀(S) satisfies Poisson's formula.     

Reducibility of lacunary polynomials,VII

Letk>1 and let be non-zero algebraic numbers contained in the field . It is shown that for almost all, in the sense of density integer vectorsn ₁,...,n _k the polynomial becomes irreducible over on dividing by the product of all factorsx–, where is a root of unity.Dedicated to Professor E. Hlawka on the occasion of his seventieth birthday     

Common invariant subspaces for collections of operators

Let be a collection of bounded operators on a Banach spaceX of dimension at least two. We say that is finitely quasinilpotent at a vectorx ₀X whenever for any finite subset of the joint spectral radius of atx ₀ is equal 0. If such collection contains a non-zero compact operator, then and its commutant have a common non-trivial invariant, subspace. If in addition, is a collection of positive operators on a Banach lattice, then has a common non-trivial closed ideal. This result and a recent remarkable theorem of Turovskii imply the following extension of the famous result of de Pagter to semigroups. Let be a multiplicative semigroup of quasinilpotent compact positive operators on a Banach lattice of dimension at least two. Then has a common non-trivial invariant closed ideal.This work was supported by the Research Ministry of Slovenia.     

Irrationalité de Valeurs Associées a l'Exponentielle de Carlitz

Lete and be the Carlitz-module analogues of their usual counterparts. We have proved in [4]-that these elements of are algebraically independent over whenq3. We study here the remaining caseq=2 and prove among other things that 1,e, are linearly independent over .

     

Skew-symmetric derivations of a complex Lie algebra

Let be a complex Lie algebra, its underlying real Lie algebra, a real form of and ·, · the euclidean product induced by the real part of an hermitian inner product on . Let aut be the Lie algebra of skew-symmetric derivations of . We give necessary and sufficient conditions to ensure that aut is composed of skew-hermitian derivations. As an application, we study holomorphy in large subgroups of isometries of Lie groups.     

Hankel operators on the weighted Bergman spaces with exponential type weights

Let denote the closed subspace of consisting of analytic functions in the unit disk . For certain class of subharmonic , the Hankel operatorH _b on with symbol is studied. Criteria for boundedness and compactness of such kind of Hankel operators are presented.R. Rochberg's research was partially supported by a grant from the National Science Foundation.     

Transvection free groups and invariants of polynomial tensor exterior algebras

Let :GGl(n, ) be a representation of a finite groupG over a field such that the ring of invariants is a polynomial algebra . It is known that in the nonmodular case (i.e., when the order of the group is not divisible by the characteristic of ), the invariants ofG acting on the tensor product of a polynomial and an exterior algebra are given by ,d denoting the exterior derivative. We show that in the modular case, the ring of invariants in is of this form if and only if is a polynomial algebra and all pseudoreflections in (G) are diagonalizable.     

Hypersurfaces of restricted type in Minkowski space

A submanifold M _n ^r of Minkowski space is said to be of restricted type if its shape operator with respect to the mean curvature vector is the restriction of a fixed linear transformation of to the tangent space of M _n ^r at every point of M _n ^r . In this paper we completely classify hypersurfaces of restricted type in . More precisely, we prove that a hypersurface of is of restricted type if and only if it is either a minimal hypersurface, or an open part of one of the following hypersurfaces: S ^k × , S _k ¹ × , H ^k × , S _n ¹ , H ⁿ , with 1kn–1, or an open part of a cylinder on a plane curve of restricted type.This work was done when the first and fourth authors were visiting Michigan State University.Aangesteld Navorser N.F.W.O., Belgium.     

On the dimension of the cartesian product of relations and orders

It is known that for incidence structures and , max , wheref dim stands for Ferrers relation. We shall show that under additional assumptions on and , both bounds can be improved. Especially it will be shown that the square of a three-dimensional ordered set is at least four-dimensional.     

Complétude des métriques lorentziennes de\mathbb{T}^2 et difféomorphismes du cercle

Let and the foliations by the null geodesics of some lorentzian metricg on the torus . We analyse how geodesic completeness properties ofg are related to the dynamics of and .     

Prime ideal decomposition inF({}^m\sqrt \mu )

LetF be an algebraic number field and F such thatx ^m– is irreducible, wherem is an integer. Let be a prime ideal inF with . The prime decomposition of in is explicitly obtained in the following cases. Case 1: , (a,m) = 1 (where means , 0 ). Case 2:m lt, wherel is a prime andl 0 . Case 3:m 0 and every prime that dividesm also dividespf–1. It is not assumed that thev ^th roots of unity are inF for anyv 2.     

Large Deviation Principle for Exchangeable Sequences: Necessary and Sufficient Condition

For an exchangeable sequence of random variables valued in a Polish space, we obtain a necessary and sufficient condition for the large deviation principles of the occupation measure L _n :=(1/n) and of the process-level empirical measures.     

Change of variables in a multiple integral for local fields

A proof of the formula for locally compact fields andC ¹-isomorphisms :UV, whereU andV are open subsets of , was never published. In this paper we give two short proofs, one of them is a more elementary variant of the other.     

Bounds for the lattice point enumerator

For the lattice point enumerator of a lattice and a convex body K we give bounds in terms of the intrinsic volumes of K and of minimal determinants of . The intrinsic volumes are the normalized Minkowski quermassintegrals and the minimal determinants are analogous functionals of .     

Operator inequalities and construction of Krein spaces

Let be a Hilbert space. A continuous positive operatorT on uniquely determines a Hilbert space which is continuously imbedded in and for which with the canonical imbedding . A Kreîn space version of this result, however, is not valid in general. This paper provides a necessary and sufficient condition for that a continuous selfadjoint operatorT uniquely determines a Kreîn space ( ) which is continuously imbedded in and for which with the canonical imbedding .     

A Note on Extremes of Concomitants of Order Statistics

Let be a sequence of identically distributed variables. We study the asymptotic distribution of , where Y _[r:n] denotes the concomitant of the rth order statistic X _r:n , corresponding to , and is held fixed while . Conditions are given for the and to have the same asymptotic behavior as that we would apply if were i.i.d. The result is illustrated with a simple linear regression model , where is a stationary sequence with extremal index .     

Sylow subgroups of finitary linear groups

In this paper we describe the structure and the conjugacy classes of Sylow p-subgroups of FGL(V, ), the group of finitary -automorphisms of the -vector space V.The Author is member of the GNSAGA.     

On the Irreducibility of Commuting Varieties Associated with Involutions of Simple Lie Algebras

Let be a reductive Lie algebra over an algebraically closed field of characteristic zero and an arbitrary -grading. We consider the variety , which is called the commuting variety associated with the -grading. Earlier it was proved by the author that is irreducible, if the -grading is of maximal rank. Now we show that is irreducible for and (E₆,F₄). In the case of symmetric pairs of rank one, we show that the number of irreducible components of is equal to that of nonzero non--regular nilpotent G ₀-orbits in . We also discuss a general problem of the irreducibility of commuting varieties.