BRST Resolution for the Principally Graded Wakimoto Module of $$\widehat{\mathfrak{s}\mathfrak{l}}_2 $$

BRST resolution is studied for the principally graded Wakimoto module of recently found in math.QA/0005203. The submodule structure is completely determined and irreducible representations can be obtained as the zero-th cohomology group.     

Finitely Valued f-Modules, An Addendum

In an -group M with an appropriate operator set it is shown that the -value set (M) can be embedded in the value set (M). This embedding is an isomorphism if and only if each convex -subgroup is an -subgroup. If (M) has a.c.c. and M is either representable or finitely valued, then the two value sets are identical. More generally, these results hold for two related operator sets ₁ and ₂ and the corresponding -value sets and . If R is a unital -ring, then each unital -module over R is an f-module and has exactly when R is an f-ring in which 1 is a strong order unit.     

Strong topologies on vector-valued function spaces

Let be a real Banach space and let E be an ideal of L ⁰ over a -finite measure space (, , ). Let (X) be the space of all strongly -measurable functions f: X such that the scalar function , defined by , belongs to E. The paper deals with strong topologies on E(X). In particular, the strong topology the order continuous dual of E(X)) is examined. We generalize earlier results of [PC] and [FPS] concerning the strong topologies.     

Extremal Solutions for Quasilinear Elliptic Inclusions in All of ℝN with State-Dependent Subdifferentials

This paper deals with quasilinear elliptic differential inclusions defined in all of ^N and governed in general by a nonpotential quasilinear elliptic operator of the Leray–Lions type and a multivalued term in form of a (nonmonotone) state-dependent subdifferential. We prove the existence of entire extremal solutions within a sector of an ordered pair of appropriately defined upper and lower solutions without imposing any condition at infinity. Therefore, standard variational methods cannot be applied here. Furthermore, due to the unboundedness of the domain and due to lack of monotonicity of the operators involved, no comparison results are available such that the problem under consideration becomes even more difficult.     

Mappings on Spaces of Continuous Functions

Let X and Y be locally compact Hausdorff spaces and T : C₀(X) C₀(Y) a ring homomorphism. We completely characterize such homomorphisms and show that if T is R-linear, then T is either C-linear or C-antilinear. In any case T is continuous and there is a continuous map : Y X such that Tf = f o , f C₀(X) (if T is C-linear) or (if T is C-antilinear). Thus, extending a result of Mólnar, we also derive the general form of an isometry T.AMS Subject Classification (2000): primary 46J05, 46E25(deceased) Passed away on 24 May 1999.     

On Norden Metrics which Are Locally Conformal to Anti-Kählerian Metrics

We build examples of Norden metrics on × S ¹, where R ^{2 n} _n is either a pseudosphere or a pseudohyperbolic space. These turn out to be locally conformal to flat anti-Kählerian metrics, strongly non anti-Kählerian, and with a parallel Lee form. Conversely, any connected complete anti-Hermitian manifold possessing these properties is shown to be locally analytically homothetic to × S ¹.     

Tight Distance-Regular Graphs

We consider a distance-regular graph with diameter d 3 and eigenvalues k = ₀ > ₁ > ... > _d . We show the intersection numbers a ₁, b ₁ satisfy

Densely Continuous Forms in Vietoris Hyperspaces

For countably paracompact normal spaces X and locally compact separable metric spaces Y, a characterization is given for the closure of the set of densely continuous forms from X to Y in the hyperspace of nonempty closed subsets of X × Y under the Vietoris topology. This shows that for such X having no isolated points, every closed subset of X × R that is dense over X can be Vietoris approximated by a semicontinuous function on X.     

Groups with Polycyclic Non-Normal Subgroups

The structure of groups in which many subgroups have a certain property X has been investigated for several choices of the property X. Groups whose non-normal subgroups satisfy certain finite rank conditions are studied in this article. In particular, a classification of groups in which every subgroup is either normal or polycyclic is given.(Dedicated to Mario Curzio on the occasion of his 70th birthday)1991 Mathematics Subject Classification: 20F16     

A Five-term Exact Sequence for Opext of Crossed Modules in Lie Algebras

Extensions of crossed modules in Lie algebras with abelian kernel are studied, particularly backward and forward induced extensions and related properties. The set Opext((U, Q, ), (R, K, )) of congruence classes of extensions of (R, K, ) by (U, Q, ) is endowed with a K-vector space structure. This K-vector space appears in a five-term natural and exact sequence associated with an extension of crossed modules.2000 Mathematics Subject Classification: 17B56, 17B99, 18G99