Transversal Twistor Spaces of Foliations

The transversal twistor space of a foliation of an even codimension is the bundle of the complex structures of the fibers of the transversalbundle of . On there exists a foliation by covering spaces of the leaves of , and any Bottconnection of produces an ordered pair of transversal almost complex structures of . The existence of a Bott connection which yields a structure ₁ that is projectable to the space of leaves isequivalent to the fact that is a transversallyprojective foliation. A Bott connection which yields a projectablestructure ₂ exists iff isa transversally projective foliation which satisfies a supplementarycohomological condition, and, in this case, ₁is projectable as well. ₂ is never integrable.The essential integrability condition of ₁ isthe flatness of the transversal projective structure of .     

Killing spinors on K?hler manifolds

In the paper Kählerian Killing spinors are defined and their basic properties are investigated. Each Kähler manifold that admits a Kählerian Killing spinor is Einstein of odd complex dimension. Kählerian Killing spinors are a special kind of Kählerian twistor spinors. Real Kählerian Killing spinors appear for example, on closed Kähler manifolds with the smallest possible first eigenvalue of the Dirac operator. For the complex projective spaces P ^2l–1 and the complex hyperbolic spaces H ^2l–1 withl>1 the dimension of the space of Kählerian Killing spinors is equal to ( ). It is shown that in complex dimension 3 the complex hyperbolic space H ³ is the only simple connected complete spin Kähler manifold admitting an imaginary Kählerian Killing spinor.     

A Helly-type theorem for simple polygons

Let be a family of simple polygons in the plane. If every three (not necessarily distinct) members of have a simply connected union and every two members of have a nonempty intersection, then {P:P in } . Applying the result to a finite family of orthogonally convex polygons, the set {C:C in } will be another orthogonally convex polygon, and, in certain circumstances, the dimension of this intersection can be determined.Supported in part by NSF grant DMS-9207019.     

Gray codes from antimatroids

We show three main results concerning Hamiltonicity of graphs derived from antimatroids. These results provide Gray codes for the feasible sets and basic words of antimatroids.For antimatroid (E, ), letJ( ) denote the graph whose vertices are the sets of , where two vertices are adjacent if the corresponding sets differ by one element. DefineJ( ;k) to be the subgraph ofJ( )² induced by the sets in with exactlyk elements. Both graphsJ( ) andJ( ;k) are connected, and the former is bipartite.We show that there is a Hamiltonian cycle inJ( )×K ₂. As a consequence, the ideals of any poset % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgznf% gDOfdaryqr1ngBPrginfgDObYtUvgaiuaacqWFpepuaaa!414C!\[\mathcal{P}\] may be listed in such a way that successive ideals differ by at most two elements. We also show thatJ( ;k) has a Hamilton path if (E, ) is the poset antimatroid of a series-parallel poset.Similarly, we show thatG( )×K ₂ is Hamiltonian, whereG( ) is the basic word graph of a language antimatroid (E, ). This result was known previously for poset antimatroids.Research supported in part by NSERC.Research supported in part by the Natural Sciences and Engineering Research Council of Canada under Grant A3379.     

Notes on Brown-McCoy-radicals for Γ-near-rings

The Brown-McCoy radical is known to be an ideal-hereditary Kurosh-Amitsur radical in the variety of zerosymmetric near-rings. We define the Brown-McCoy and simplical radicals, and , respectively, for zerosymmetric -near-rings. Both and are ideal-hereditary Kurosh-Amitsur radicals in that variety. IfM is a zerosymmetric -near-ring with left operator near-ringL, it is shown that , with equality ifM has a strong left unity. is extended to the variety of arbitrary near-rings, and and are extended to the variety of arbitrary -near-rings, in a way that they remain Kurosh-Amitsur radicals. IfN is a near-ring andA N, then , with equality ifA if left invariant.     

Symplectic Reduction and the Homogeneous Complex Monge–Ampère Equation

A Riemannian manifold ( ⁿ , g) is said to be the center of thecomplex manifold ⁿ if is the zero set of a smooth strictly plurisubharmonic exhaustion function ² on such that is plurisubharmonic and solves theMonge–Ampère equation ( ) ⁿ = 0 off , and g is induced by the canonical Kähler metric withfundamental two-form ². Insisting that be unbounded puts severe restrictions on as acomplex manifold as well as on ( , g). It is an open problemto determine the class Riemannian manifolds that are centers of complexmanifolds with unbounded . Before the present work, the list of knownexamples of manifolds in that class was small. In the main result of thispaper we show, by means of the moment map corresponding to isometric actionsand the associated bundle construction, that such class is larger than originally thought and contains many metrically and diffeomorphically`exotic' examples.     

Towards a model theory for 2-hyponormal operators

We introduce the notion ofweak subnormality, which generalizes subnormality in the sense that for the extension ofT we only require that hold forf ; in this case we call a partially normal extension ofT. After establishing some basic results about weak subnormality (including those dealing with the notion of minimal partially normal extension), we proceed to characterize weak subnormality for weighted shifts and to prove that 2-hyponormal weighted shifts are weakly subnormal. Let { _n } _n=0 be a weight sequence and letW denote the associated unilateral weighted shift on . IfW is 2-hyponormal thenW is weakly subnormal. Moreover, there exists a partially normal extension on such that (i) is hyponormal; (ii) ; and (iii) . In particular, if is strictly increasing then can be obtained as

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 causality in commutant lifting theorem. I

Two functionals (A) and for an operatorA were introduced in [11] for the study of causality in commutant lifting theory. In this paper we give sufficient and necessary conditions for in a special case. We prove that in this case , and we show by some examples related to nonlinear system control that is the best constant in our inequality.     

A structure theorem for weak buildings of spherical type

Following earlier work of Tits [8], this paper deals with the structure of buildings which are not necessarily thick; that is, possessing panels (faces of codimension 1) which are contained in two chambers, only. To every building , there is canonically associated a thick building whose Weyl group W( ) can be considered as a reflection subgroup of the Weyl group W() of . One can reconstruct from together with the embedding W( ) W(). Conversely, if is any thick building and W any reflection group containing W( ) as a reflection subgroup, there exists a weak building with Weyl group W and associated thick building .     

Nilpotent action on the KDV variables and 2-dimensional Drinfeld-Sokolov reduction

We note that a version with spectral parameter of the Drinfeld-Sokolov reduction gives a natural mapping from the KdV phase space to the group of loops with values in : affine nilpotent andA principal commutative (or anisotropic Cartan) subgroup; this mapping is connected to the conserved densities of the hierarchy. We compute the Feigin-Frenkel action of (defined in terms of screening operators) on the conserved densities in thesl ₂ case.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 98, No. 3, pp. 375–378, March, 1994.     

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 .     

Topological and bornological characterisations of ideals in von Neumann algebras: I

Suppose is a von Neumann algebra on a Hilbert space and is any ideal in . We determine a topology on , for which the members of that are to norm continuous are exactly those in ; and a bornology on such that the elements of which map the unit ball to an element of , equivalently those members of that are norm to bounded, are exactly those in . This is achieved via analogues of the notions of injectivity and surjectivity in the theory of operator ideals on Banach spaces.     

On a theorem of Seidel and Walsh

Given a sequence ( _n ) _n in with there are functions such that , is a dense subset of , and the set of functions with this property is residual in . We will show that in and some related Banach spaceX there are functionsf with is dense in , and we will give a sufficient condition when the set of such functions is residual inX.     

Positive elements in the algebra of the quantum moment problem

Summary Let denote the extended Weyl algebra, , the Weyl algebra. It is well known that every element of of the formA=B _k ^* B _k is positive. We prove that the converse implication also holds: Every positive elementA in has a quadratic sum factorization for some finite set of elements (B _k ) in . The corresponding result is not true for the subalgebra . We identify states on which do not extend to states on . It follows from a result of Powers (and Arveson) that such states on cannot be completely positive. Our theorem is based on a certain regularity property for the representations which are generated by states on , and this property is not in general shared by representations generated by states defined only on the subalgebra .Work supported in part by the NSF     

Operators of fibered groups

Let (G, ) denote a finite groupG with fibration . The group Aut (G, ) of operators of (G, ) is closely related to the group of collineations of (G, ). In this paper we investigate the geometric properties imposed on (G, ) by requiring that Aut (G, )=AutG. We find that in many instances this algebraic property restricts the geometry to a very special form.Dedicated to Professor Helmut Karzel on the occasion of his 60th birthday.     

On periodic groups of automorphisms of extremal groups

It is proved that if a periodic group has an extremal normal divisor , determining a complete abelian factor group , then the center of the group contains a complete abelian subgroup , satisfying the relation and intersecting on a finite subgroup. It is also established with the aid of this proposition that every periodic group of automorphisms of an extremal group is a finite extension of a contained in it subgroup of inner automorphisms of the group .Translated from Matematicheskie Zametki, Vol. 4, No. 1, pp. 91–96, July, 1968.     

On some properties of the metric subalgebras ofℓ ∞

The objects studied are the subalgebras of which contain c_o. These are isometrically isomorphic to the algebras C( ) where is a compactification of a discrete denumerable set N . It is shown: 1) If is metric then there is a projection of norm 1, P: C( ) C( ) with kernel c_o defined by PF = f o where is a retraction of onto = – N . 2) If is metric, then the group of homeomorphisms of is isomorphic to a complete group of permutations of the natural numbers . 3) The group of homeomorphisms of a compact metric space is the homomorphic image of a complete group of permutations of ("complete" means "no outer automorphisms, trivial center").     

Tensor invariants of the Lie algebra sl2(ℂ[t]) and fundamental representations of the Lie algebras\hat p_{2n}

Generators of the space of tensor invariants of the Lie algebra Sl₂([t]) are constructed. It is proved that the restrictions of a spinor representation of the affine Lie algebra to and form a dual pair. A realization of the fundamental representations of the Lie algebra is obtained.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, Akad. Nauk SSSR, Vol. 172, pp. 137–144, 1989.     

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 .