In this paper a further refinement of Dade's projective conjecture, due to Boltje, is presented. This new statement includes ideas first published by Isaacs and Navarro as well as the recent contractibility version of Alperin's conjecture introduced by Boltje. Leaning heavily on the work of Robinson, weaker forms of the conjecture are proved in the case of p-solvable groups. 相似文献
This work describes the syntheses of a new poly(amidoamine) (PAMAM) dendrimer family possessing a disulfide function (cystamine) in its core. Traditional redox-chemistry associated with the disulfide core in these dendrimer structures, provides a versatile strategy for designing unique sizes, shapes and controlling the regio-disposition of chemical groups on the surface of these dendrimers. Various single site, sulfhydryl functionalized dendron reactants may be generated in situ, under standard reducing conditions (i.e. dithiothreitol (DTT)). Facile control of size, shape and chemical functionality placement involves covalent hybridization of these single point, sulfhydryl reactive dendron components. This is accomplished by re-oxidation in the presence of air, to yield generation/surface chemistry differentiated cross-over products which may be isolated by preparative thin layer or column chromatography. Differentiated cystamine core dendrimers derived from combination and permutation of lower generation (i.e. Gen.=0-3) sulfhydryl functionalized dendrons possessing amino, hydroxyl, acetamido or dansyl surface groups, were synthesized and isolated. They were characterized by a variety of methods including; 13C NMR, capillary electrophoresis (CE), gel electrophoresis (PAGE), thin layer chromatography (TLC) and electrospray (ES) or matrix assisted laser desorption ionization (MALDI-TOF) mass spectrometry. This general strategy has broad implications for the systematic size, shape and regio-chemical control of a wide range of dendritic nanostructures, many of which may be designed to mimic the sizes, shapes and regio specific chemo-domains observed for globular proteins. 相似文献
Tensor product of irreducible modules of highest weight over a semi-simple quantum group is completely reducible if and only if a natural contravariant form is non-degenerate when restricted to the span of singular vectors. We express this restriction through the extremal projector of the quantum group providing a computationally feasible criterion for complete reducibility of tensor products. 相似文献
It is shown how to represent algebraically all functions that have a zero sum on all -dimensional subspaces ofPG(n,q) or ofAG(n,q). In this way one can calculate the dimensions of related codes, or one can represent interesting sets of points by functions. 相似文献
A weakly continuous, equicontinuous representation of a semitopological semigroup on a locally convex topological vector space gives rise to a family of operator semigroup compactifications of , one for each invariant subspace of . We consider those invariant subspaces which are maximal with respect to the associated compactification possessing a given property of semigroup compactifications and show that under suitable hypotheses this maximality is preserved under the formation of projective limits, strict inductive limits and tensor products.
A (right -) module is said to be a Whitehead test module for projectivity (shortly: a p-test module) provided for each module , implies is projective. Dually, i-test modules are defined. For example, is a p-test abelian group iff each Whitehead group is free. Our first main result says that if is a right hereditary non-right perfect ring, then the existence of p-test modules is independent of ZFC + GCH. On the other hand, for any ring , there is a proper class of i-test modules. Dually, there is a proper class of p-test modules over any right perfect ring.
A non-semisimple ring is said to be fully saturated (-saturated) provided that all non-projective (-generated non-projective) modules are i-test. We show that classification of saturated rings can be reduced to the indecomposable ones. Indecomposable 1-saturated rings fall into two classes: type I, where all simple modules are isomorphic, and type II, the others. Our second main result gives a complete characterization of rings of type II as certain generalized upper triangular matrix rings, . The four parameters involved here are skew-fields and , and natural numbers . For rings of type I, we have several partial results: e.g. using a generalization of Bongartz Lemma, we show that it is consistent that each fully saturated ring of type I is a full matrix ring over a local quasi-Frobenius ring. In several recent papers, our results have been applied to Tilting Theory and to the Theory of -modules.
LetR be a ring with unit and invariant basis property. In [1], the authors define a functorK(_;R):TOP/LIPc-LPEP by combining the open cone construction of [7] with a geometric module construction and show this functor is a homology theory. This paper shows that if attention is restricted to objects TOP/LIPc with a homotopy colimit structure, then the functorK(_;R) is a Quinn homology theory, In particular, for each having a homotopy colimit structure,K(;R) is a homotopy colimit in the category of -spectra. Furthermore, the constituent spectra of this homotopy colimit are obtained naturally from the fibres of .Partially supported by the National Science Foundation under grant number DMS88-03148.Partially supported by the SNF (Denmark) under grant number 11-7792. 相似文献
Irreducible covariant tensor modules for the Lie supergroups GL(m/n) and the Lie superalgebras gl(m/n) and sl(m/n) are obtained through the use of Young tableaux techniques. The starting point is the graded permutation action, first introduced by Dondi and Jarvis, on Vl. The isomorphism between this group of actions and the symmetric group Sl enables the graded generalization of the Young symmetrizers, and hence of the column relations and Garnir relations, to be made. Consequently, corresponding to each partition of l an irreducible GL(m/n) module may be obtained as a submodule of Vl. A basis for the module labeled by the partition is provided by GL(m/n)–standard tableaux of shape defined by Berele and Regev. The reduction of an arbitrary tableau to standard form is accomplished through the use of graded column relations and graded Garnir relations. The standardization procedure is algorithmic and allows matrix representations of the Lie superalgebras gl(m/n) and sl(m/n) to be constructed explicitly over the field of rational numbers. All the various steps of the standardization algorithm are exemplified, as well as the explicit construction of matrices representing particular elements of gl(m/n) and sl(m/n). 相似文献