by Lewis, Mark L.

Let G be a solvable group with five character degrees. Suppose that there is some prime p so that G/

^p
(G) is not Abelian. Also, assume that cd(G) contains a degree that is not divisible by p. Under these hypotheses, we show that the derived length of G is at most 4.

DOI: 10.1023/A:1016535504003
Print publication date: 8/1/2002
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by König, S.; Mazorchuk, V.

We prove that the following two categories of sl(n,C)-modules are equivalent: (1) the category of modules with integral support filtered by submodules of Verma modules and complete with respect to Enright’s completion functor; (2) the category of all subquotients of modules F⊗M, where F is a finite-dimensional module and M is a fixed simple generic Gelfand–Zetlin module with integral central character. Our proof is based on an explicit construction of an equivalence which, additionally, commutes with translation functors. Finally, we describe some applications of this both to certain generalizations of the category O and to Gelfand–Zetlin modules.

DOI: 10.1023/A:1016531419024
Print publication date: 8/1/2002
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by Futorny, V.; König, S.; Mazorchuk, V.

We construct a generalization of the BGG-category O, whose blocks correspond to standardly stratified algebras. We prove reciprocity formulae in these categories and present two classes of examples.

DOI: 10.1023/A:1016579318115
Print publication date: 8/1/2002
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by Domokos, M.; Zubkov, A. N.

We prove that the results of Le Bruyn and Procesi on the varieties parameterizing semisimple representations of quivers hold over an algebraically closed base field of arbitrary characteristic.

DOI: 10.1023/A:1016554601277
Print publication date: 8/1/2002
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by Lanzmann, Emmanuel

R. B. Zhang found a way to link certain formal deformations of the Lie algebra o(2l+1) and the Lie superalgebra osp(1,2l). The aim of this article is to reformulate the Zhang transformation in the context of the quantum enveloping algebras à la Drinfeld and Jimbo and to show how this construction can explain the main theorem of Gorelik and Lanzmann: the annihilator of a Verma module over the Lie superalgebra osp(1,2l) is generated by its intersection with the centralizer of the even part of the enveloping algebra.

DOI: 10.1023/A:1016550528593
Print publication date: 8/1/2002
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by Burke, Kevin; Prest, Mike

It was a conjecture of the second author that the Cantor–Bendixson rank of the Ziegler spectrum of a finite-dimensional algebra is either less than or equal to 2 or is undefined. Here we refute this conjecture by describing the Ziegler spectra of some domestic string algebras where arbitrary finite values greater than 2 are obtained. We give a complete description of the Ziegler and Gabriel–Zariski spectra of the simplest of these algebras. The conjecture has been independently refuted by Schröer who, extending his work (1997) on these algebras, computed their Krull–Gabriel dimension.

DOI: 10.1023/A:1016581927685
Print publication date: 8/1/2002
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