Invariant ideals of twisted crossed products

We will prove a result concerning the inclusion of non-trivial invariant ideals inside non-trivial ideals of a twisted crossed product. We will also give results concerning the primeness and simplicity of crossed products of twisted actions of locally compact groups on -algebras. Received: 25 January 2002; in final form: 22 May 2002/Published online: 2 December 2002 This work is partially supported by Hong Kong RGC Direct Grant.     

A remark on Mansfield's imprimitivity theorem

We show that the Morita equivalence part of Mansfield's Imprimitivity Theory can be obtained by Green's Imprimitivity Theorem (and duality theory).

     

The synthesis and reactivity of the heptanuclear dianion [Os7(CO)20]2− including the synthesis and structural characterizations of the compounds [Os7(CO)20(AuPEt)3 2] and [Os8(CO)20(η6-C6H6]

Reduction of the heptaosmium cluster [Os₇(CO)₂₁] With [Et₄N][NH₄) gives the cluster dianion [Os₇(CO)₂₀]^2–,1, in high yield. The reaction of the dianion with [AuPR ₃Cl] (R=Et or Ph) in the presence of TlPF₆ forms [Os₇((CO)₂₀(AuPR ₃)₂] [R=Et (2a);R = Ph(2b)] in 80% yield, while the corresponding reaction with (Os(C₆H₆)(CH₃CN)₃]²⁺ gives [Os₈(CO)₂₀ ( ⁶-C₆H₆)] (3) in reasonable yield (ca. 30%). The dianion,1, and the clusters2 and3 have been fully characterized by bout spectroscopic and crystallographic methods. The crystal structure of the [Ph₄P]⁺ salt of1 shows that the metals in the anion adopt a capped octahedral geometry, with all twenty carbonyl ligands in terminal sites. The metal core geometry in2a is best described as a tricapped octahedron, and is based on the structure of the dianion1 with two adjacent octahedral faces capped by the Au atoms of the two AuPEt₃ groups. In a similar fashion, the geometry of3 is related to that of1 with the addition of an Os(C₆H₆) unit capped to a triangular face, to give a bicapped octahedral framework.     

Chern forms,chern numbers and curvature conditions on a Kähler-Einstein surface

In this paper we considered curvature conditions on a Kähler-Einstein surface of general type. In particular we showed that it has negative holomorphic sectional curvature if theL ²-norm of (3C ₂ ?C ₁ ² )/C ₁ ² is sufficiently small, whereC ₁ andC ₂ are the first and second Chern classes of the surfaces. This generalizes a result of Yau on the uniformization of Kähler-Einstein surfaces of general type and with 3C ₂ ?C ₁ ² = 0. Also in the process, we obtain a necessary condition in terms of an inequality between Chern numbers for a Kähler-Einstein metric to have negative holomorphic sectional curvature.     

Some new domains with complete Kähler metrics of negative curvature

We add to the known examples of complete Kähler manifolds with negative sectional curvature by showing that the following three classes of domains in euclidean spaces also belong: perturbations of ellipsoidal domains in ?ⁿ, intersections of complex-ellipsoidal domains in ?², and intersections of fractional linear transforms of the unit ball in ?². In the process, we prove the following theorem in differential geometry: in the intersection of two complex-ellipsoidal domains in ?², the sum of the Bergman metrics is a Kähler metric with negative curvature operator.     

Crystal engineering of urea alpha-network via I...O2N synthon and design of SHG active crystal N-4-iodophenyl-N'-4'-nitrophenylurea

Crystalline nitrodiphenyl ureas adopt the N-H...O tape alpha-network only when stabilization accrues from the I...O(2)N or C[triple bond]C-H...O(2)N synthon, otherwise the ureanitro motif is preferred; soft, weak interactions can direct polar self-assembly in strong N-HO hydrogen-bonded crystals.     

Generation and Reactivity of a One-Electron-Oxidized Manganese(V) Imido Complex with a Tetraamido Macrocyclic Ligand

The synthesis and X-ray structure of a new manganese(V) mesitylimido complex with a tetraamido macrocyclic ligand (TAML), [Mn^V(TAML)(N-Mes)]⁻ ( 1 ), are reported. Compound 1 is oxidized by [(p-BrC₆H₄)₃N ]^+.[SbCl₆]⁻ and the resulting Mn^VI species readily undergoes H-atom transfer and nitrene transfer reactions.     

2,4,6-Tris(4-nitrophenoxy)-1,3,5-triazine: a hexagonal host framework stabilised by the NO2-trimer supramolecular synthon

The title molecule forms a honeycomb network of molecular and nitro-trimer synthons with guest species included in the hexagonal voids.     

Cohomology of Hopf C*-Algebras and Hopf Von Neumann Algebras

We define two canonical cohomology theories for Hopf C^*-algebrasand for Hopf von Neumann algebras (with coefficients in theircomodules). We then study the situations when these cohomologiesvanish. The cases of locally compact groups and compact quantumgroups are considered in more detail. E-mail: c.k.ng{at}qub.ac.uk2000 Mathematical Subject Classification: primary 46L05, 46L55;secondary 43A07, 22D25.     

Hydrogen-bonded anionic rosette networks assembled with guanidinium and C3-symmetric oxoanion building blocks

Two premeditated anionic rosette-layer architectures have been constructed using guanidinium and ubiquitous C3-symmetric oxoanions that carry unequal charges, employing bulky organic cations as interlayer templates. The undulate guanidinium-carbonate network occurs in 4[(C2H5)4N+].8[C(NH2)3+].3(CO3)2-.3(C2O4)2-.2H2O, in which the disordered (C2H5)4N+ guests are accommodated in pouches and channels within a complex three-dimensional hydrogen-bonded host framework. In [(C2H5)4N+]2.[C(NH2)3+].[1,3,5-C3H3(COO-)3].6H2O, ordered (C2H5)4N+ cations are sandwiched between planar guanidinium-trimesate host layers whose honeycomb cavities are tightly fitted with flattened-chair (H2O)6 clusters of symmetry 2.