Let H be a semisimple Hopf algebra over an algebraically closed field k. It is assumed that either char k = 0 or char k > dimH . Semisimplicity of H means that H is a semisimple left H-module. In that case H has finite dimension. Throughout the paper we shall keep to notations from [M]. For example H stands for the dual Hopf algebra with the natural pairing 〈−,−〉 : H ⊗ H → k. The algebra H is a...

Let M be a space of weakly*-measurable functions F : ? B(H) on measure (?,?,?), for which the function F*F is Gel'fand integrable and integral d? nuclear operator Hilbert H. We show that H*-module contains an orthonormal basis.

This paper describes a system that uses AI planning and representation techniques as the core of a decision support system.* The planning technology is supplemented with other AI and non-AI technologies. The overall system and initial application domain, military operations planning, are described first. We then describe the integration of SIPE-2, a generative planning system, with three indepe...

let a be a banach algebra and e be a banach a-bimodule then s = a  e, the l1-direct sum of a and e becomes a module extension banach algebra when equipped with the algebras product (a; x):(a′; x′) = (aa′; a:x′ + x:a′). in this paper, we investigate △-amenability for these banach algebras and we show that for discrete inverse semigroup s with the set of idempotents es, the module extension bana...

let $r$ be a commutative ring with identity and $m$ be a finitely generated unital $r$-module. in this paper, first we give necessary and sufficient conditions that a finitely generated module to be a multiplication module. moreover, we investigate some conditions which imply that the module $m$ is the direct sum of some cyclic modules and free modules. then some properties of fitting ideals of...

A Fock space is introduced which admits an action of a quantum group of type A supplemented with some extra operators. The canonical and dual canonical basis of the Fock space are computed and then used to derive the finite-dimenisonal tilting and irreducible characters for the Lie superalgebra osp(2|2n). We also determine all the composition factors for the symmetric tensors of the natural osp...

Preface These notes are based on a course given at the Tata Institute of Fundamental Research in the beginning of 1990. The aim of the course was to describe the solution by O. Mathieu of some conjectures in the representation theory of semi-simple algebraic groups. These conjectures concern the inner structure of dual Weyl modules and some of their analogues. Recall that if G is a (connected, ...

Nonfastidious aerobic gram-negative bacilli (GNB) are commonly isolated from blood cultures. The feasibility of using an electrochemical method for direct antimicrobial susceptibility testing of GNB in positive blood cultures was evaluated. An aliquot (10 microliter) of 1:10-diluted positive blood cultures containing GNB was inoculated into the Bactometer module well (bioMérieux Vitek, Hazelwoo...

Let G be an affine algebraic group over an algebraically closed field k and let H be a closed subgroup of G. If V is a rational H-module (a comodule for the coordinate ring of H) there is a now well-known notion of an induced module VI G for G, defined as the space Morph/~(G, V) of all H-equivariant morphisms from G to a finite dimensional subspace of V, with obvious G-action. The question aris...