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The aim of this paper is to prove that any real or complex Lie algebra admitting a non-singular prederivation is necessarily a nilpotent Lie algebra. As to the reciprocal statement, an example is given of a nilpotent Lie algebra with only singular prederivations.

In this paper for every p > 0 the universal family of the hypersurfaces of degree 2 p and dimension 3 invariant under a certain action of the group of p -th roots of unity is considered. The maximal abelian rational sub-Hodge structure of weight 3 is investigated on the general element and the general Grothendieck-Hodge conjecture is checked for the general point of some special sub-families.

Claasen and Goldbach introduced a class of finite rings with a field-like property. In this paper we show that it coincides with the class of finite Frobenius rings.

In the present paper, we give a proof for the existence of this invariant, called the Serre-Rost invariant in the sequel, that is more elementary than Rost’s. Our approach takes up another suggestion of Serre [26] and is inspired by the concept of chain equivalence [23, p. 143] in the algebraic theory of quadratic forms (see 4.2, 4.13 for details). The proof we obtain in this way works uniformly in all characteristics except 3. (In characteristic 3, Serre has shown how to define the invariant in a different way; see 4.24 for comments). In order to make our presentation comparatively selfcontained, we include without proof some preliminary material from elementary Galois cohomology (Sec. 1) and the theory of algebras of degree 3 (Sec. 2) that will be needed in the subsequent development. Rather than striving for maximum generality, we confine ourselves to what is indispensable for

A Sturmian bisequence S is a subset of ℤ such that the numbers of elements of S in any two intervals of equal lengths differ by at most 1. A complementary triple of bisequences is a set of three bisequences such that every integer belongs to exactly one bisequence. In the paper a question of Loeve is answered by giving a characterization of all complementary triples of Sturmian bisequences.

It is shown in this paper in an elementary, intrinsic way that a positive definite quadratic polynomial in an Archimedean f-algebras has a negative discriminant. As a corollary, a Schwarz inequality is obtained for positive linear mappings between Archimedean f-algebras, both real and complex.

The approximate point spectrum σa(T) of a selfadjoint operator T on a nontrivial separable Hilbert space is examined constructively with the help of the functional calculus for T. In particular, it is proved that σa(T) is compact if and only if ∥f(T)∥ can be computed for each f in C[−b, b], where b > 0 is a bound for T. The paper culminates in a full constructive analysis of the spectrum of a compact selfadjoint operator with infinite-dimensional range. Brouwerian examples show that the results are the best possible in the constructive setting.

By forming tensor products we construct natural examples of non-reflexive (Section 2) and nonspherically complete (Section 3) closed subspaces of the non-archimedean space l ∞ . Also, we study (Section 4) conditions under which two spherically complete Banach spaces are isomorphic; as an application we describe the spherical completion of the subspaces of l ∞ constructed in the paper.

We study multi-dimensional maps on bounded domains of R d satisfying the finite range structure (FRS) condition, which leads us to countable state sofic systems. Such maps admit σ-finite ergodic invariant measures equivalent to Lebesgue measures under the local Renyi condition. In this paper we show that several ergodic properties still hold even if such invariant measures are infinite. We also investigate the validity of Rohlin's entropy formula and of a variational principle for entropy.

Let T = {T(t)}t ≥ 0 be a C0-semigroup on a Banach space X. In this paper, we study the relations between the abscissa ωLp(T) of weak p-integrability of T (1 ≤ p < ∞), the abscissa ωpR(A) of p-boundedness of the resolvent of the generator A of T (1 ≤ p ≤ ∞), and the growth bounds ωβ(T), β ≥ 0, of T. Our main results are as follows. 1.(i) Let T be a C0-semigroup on a B-convex Banach space such that the resolvent of its generator is uniformly bounded in the right half plane. Then ω1 − ϵ(T) < 0 for some ϵ > 0.2.(ii) Let T be a C0-semigroup on Lp such that the resolvent of the generator is uniformly bounded in the right half plane. Then ωβ(T) < 0 for all β>¦1p − 1p′¦, 1p + 1p′ = 1.3.(iii) Let 1 ≤ p ≤ 2 and let T be a weakly Lp-stable C0-semigroup on a Banach space X. Then for all β>1p we have ωβ(T) ≤ 0.Further, we give sufficient conditions in terms of ωqR(A) for the existence of Lp-solutions and W1,p-solutions (1 ≤ p ≤ ∞) of the abstract Cauchy problem for a general class of operators A on X.

In [NR] the authors introduced the notion of superstable operators on a Banach space E using ultrapowers Eu of E. In [HR] this notion was extended to strongly continuous one-parameter semigroups again by means of ultrapowers. It is the aim of the present paper to give an equivalent intrinsic definition of superstability (without the reference to ultrapowers). This definition allows us to improve the results of [NR] as well as of [HR]. We apply our results to semigroups of positive linear operators on Banach lattices and C ∗ - algebras , respectively.

In this paper we study the 1-dimensional family Г of lines on the Gushel' threefold X = X∼10 (the Fano threefold of degree 10, of 2-nd kind). We show that, in case X is generic, Г is a two-sheeted unbranched covering of a smooth plane curve Г0 of degree 10. The incidence correspondence Σ ⊆ S2Г of intersection of lines on X gives rise to a generalized Prym variety P(Г, Σ) which is isomorphic to the intermediate jacobian of X. Let Y ⊆ P6 be the del Pezzo threefold. Then the natural double covering π : X → Y defines a two-sheeted covering Z of the universal P1-bundle for the family of lines on Y. The Prym variety P(Г, Г0) is isomorphic to the intermediate jacobian of Z.

The object of study of this paper is the asymptotic behaviour of sequences { M n } n ≥1 of square matrices with real or complex entries. Two decomposition theorems are treated. These give conditions under which a sequence of non-singular square matrices whose terms are block-diagonal (diagonal, respectively) matrices plus some perturbation term can be transformed into a sequence { F −1 n +1 M n F n } n ≥1 whose terms are block-diagonal (diagonal) and where the sequence { F n } n ≥1 converges to the identity. In the first section we introduce the concept of a matrix recurrence and some further notation. In §2 we present the first of the two decomposition theorems. As an application, we present, in §3, a generalization of the Theorem of Poincare-Perron for linear recurrences, and in §4 we prove a decomposition theorem for matrix sequences that are the sum of a sequence of diagonal matrices and some (small) perturbation term. In the final section we use the second decomposition theorem to derive a result concerning the solutions of matrix recurrences in case the matrices converge fast to some limit matrix. All our results are quantitative as well.

There is an explicit resolution of an irreducible polynomial module for the general linear group , due to A.V. Zelevinskii and also K. Akin, which realizes the Jacobi-Trudi expansion of the corresponding Schur function. That resolution lies in the category of polynomial representations, i.e., all the terms in the resolution are polynomial. This paper constructs several complexes from the BBG resolution of the trivial one-dimensional representation, for any reductive group G over a ground field of characteristic zero, obtaining thereby analogues of the Zelevinskii-Akin resolution for the rational representation theory of such G.

Let μ → =(μ 1 …μ n ) be a vector measure on a measurable space (ω F ) such that each μi is finite. The measures are allowed to have atoms. In this paper conditions on μ → are given under which the matrix-k-range MR k ( μ → )={(μ i (P j )) n i =1 k j =1:{P j } k j =1 is a measurable partition of Ω} is convex. This will lead to conditions on μ → under which the partition-range PR ( μ → )={(μ 1 (P 1 …μ n (P n )):{P i } n i =1 is a measurable partition of ω} and the range R ( μ → )={(μ 1 (B)…μ n (B)):B∈ F } are convex. The results (i.e. Theorem 2.7 and Theorem 2.8) are generalizations of Lyapounov's Theorem.

It is our purpose to clarify the structure of the solvable finite groups whose subgroups of equal order are conjugate. In [l], A. Bensa’id and this author suc- ceeded in determining the structure of the non-solvable finite groups satisfying that property up to that of some solvable finite groups sharing that property. All groups in this paper will be

Ol'shanskiǐ's semigroup plays a prominent role in the discussion of symmetric spaces. There are two important applications: the construction of the discrete series in representation theory and analysis on symmetric spaces. In this article the notion of an Ol'shanskiǐ wedge in a symmetric Lie algebra is defined. The tangent wedge of Ol'shanskiǐ's semigroup is an example of such a wedge. In Section 1 of this paper, a geometric characterization of Ol'shanskiǐ wedges is given and their relation to special Lie wedges is established. Section 2 deals with invariant Ol'shanskiǐ wedges and Ol'shanskiǐ semialgebras. We give a complete classification of symmetric Lie algebras supporting invariant Ol'shanskiǐ wedges, resp., Ol'shanskiǐ semialgebras.

Periodic modules are modules which admit periodic projective resolutions. In this paper it is shown that under suitable conditions periodic modules over the restricted enveloping algebra of a graded restricted Lie algebra admit filtrations in terms of intermediate (Verma) modules. Moreover, using filtrations results about determining projectivity of modules by detecting projectivity upon restriction to certain subalgebras are given for graded Lie algebras.

This paper deals with intersections of double cosets on a connected algebraic group. Under appropriate hypotheses, we show that such intersections are transversal and are smooth irreducible varieties. We also show that the closure of the intersection is the intersection of the closures.

Completing the description of the possible radii of convergence of q-series F(z)=1+∑j=1∞(∏k=1j(A-qk))zj, it is shown in this paper that, for any given 1≤R≤∞ there is a q-series with A=exp(2πiα), q=exp(2πiβ) such that its radius convergence is R. If α is a rational number, then for any irrational β, the radius is always 1.

This is the second paper of both authors on the subject indicated in the title. Cyclotomic schemes are association schemes the relations R i of which are {( x , y ) | y − xϵC i }, where the C i are the orbits of a given group of units of a finite ring. We call a commutative ring F admissible if there is a character χ of F + such that every character ω of F + can be found by the rule ω( x )=χ( ax ) for a well-chosen a ϵ F . For commutative, admissible rings the 2-class and 3-class cases are completely treated, and the results are applied to difference set theory.

The semigroup version of Lie's Third Fundamental Theorem asserts that each strictly positive cone and each finite-dimensional Lie wedge is a tangent wedge of some local semigroup. This paper investigates the question whether this local semigroup can be embedded into a global topological semigroup in such a fashion that the embedding preserves all existing products and its image is open. In the case of a strictly positive cone (in particular a finite-dimensional pointed cone) this question will be answered affirmatively. This result contrasts the situation of open embeddings into global subsemigroups of Lie groups, where counterexamples even in low-dimensional Lie groups occur. In the finite-dimensional case a homotopy-like congruence on the semigroup of conal curves induces a quotient semigroup (called conal path semigroup) which also solves the topological embedding problem.

In this paper we construct a compactification of the moduli space Bn*=(P22⧹Δ)⧸PGL(3)of n-point configuration in the plane in general position modulo linear transformations. This compactification Bn is an analogue to the space of n-pointed trees of projective lines and a generalization of a compactification of orbit spaces of more general group actions. We relate the fibres of the universal n-point configuration Fn→Bn to schemes associated with the Bruhat-Tits Building and give explicit descriptions in the cases n=5 and n=6.

In this paper we present an elementary proof of a general duality result for precompact sets which can be considered as a far-reaching generalization of a well-known result of Grothendieck on precompactness in dual systems. It is then shown that a number of known results can be deduced from it, amongst others a general form of the Arzela-Ascoli theorem and Grothendieck's duality theorem itself.

A bounded function f from an abelian group G into a complete nonarchimedean valued field K is said to be almost periodic (fϵ AP(G→K)) if its translates form a compactoid in the uniform topology. The goal of this paper is the theorem below.

In this paper, we consider the boundary M of a weakly pseudoconvex domain in a Stein manifold. We point out a striking difference between the local cohomology and the global cohomology of M, and illustrate this with an example. We also discuss the first and second Cousin problems, and the strong Poincaré problem for CR meromorphic functions on the weakly pseudoconvex boundary M.