On the stability of weight spaces of enveloping algebra in prime characteristic

By the result of Dixmier, any weight space of enveloping algebra of Lie algebra L over a field of characteristic 0 is adL stable. In this paper we will show that this result need not be true, if F is replaced by a field of prime characteristic. A condition will be given, so a weight space will be adL stable

Abhandlungen aus dem Mathematischen Seminar der Hamburgischen Universität

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37 elementare axiomatische Charakterisierungen des reellen Zahlkoerpers

enl. ed.Available from TIB Hannover: RR 9398(87) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Frobenius groups with many involutions

We consider a special class of Frobenius Groups, which generalizes the class of sharply 2-transitive groups in such a way that the construction of a neardomain can be generalized to the construction of a K-loop. The group then is shown to be a quasidirect product of that K-loop by a suitable automorphism group. The major advantage of this point of view is the existence of examples which are hoped to shed some light on the still open problem of the existence of proper neardomains. (orig.)SIGLEAvailable from TIB Hannover: RR 9398(84) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Dependence on the spin structure of the Dirac spectrum

SIGLEAvailable from TIB Hannover: RR 9398(93) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Mitteilungen aus dem Mathematischen. Seminar Giessen.

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Representations of Lie colour algebras

The main goal of this paper is to lay the foundation for studying the representations of (restricted) Lie colour algebras and relate this to its structure and properties of their (restricted) universal enveloping algebras. Since there are not too many results in the literature, the paper starts more or less from the beginning but does not always give all the details. It also concentrates on questions related to complete sets and tensor products and the development of the arguments quite often is motivated by the ungraded case. In the first section several results on the Jacobson colour ideal are provided which are well-known in the ungraded case. Moreover, a colour version of a result of Steinberg which shows the significance of complete sets of modules is established. Here it is not necessary that the grading is commutative. In general, it was tried to adapt the assumptions on the grading to the investigated topics. The second section provides some abstract results on relating tensor products to being invariant under the comultiplication. The third and the fifth section are devoted to some elementary results on the structure and representation theory of Lie colour algebras resp. restricted Lie colour algebras. Both sections are followed by a first of complete sets. In particular, a theorem of Burnside is generalized to restricted Lie colour algebras and some applications to the blocks of supersolvable restricted Lie colour algebras are given. Finally, in the last section some of the methods are applied to characterize p-reductive restricted Lie colour algebras in several ways as well as to characterize finite-dimensional restricted Lie colour algebras whose semisimple restricted modules are closed under tensor products. (orig.)SIGLEAvailable from TIB Hannover: RR 9398(79) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

The early development of the representation theory of semisimple Lie groups: A. Hurwitz, I. Schur, H. Weyl

Any historical development takes place inside a complicated network of interactions of the most various kinds. This is especially true of Hermann Weyl's celebrated early work on the representation theory of compact and complex Lie groups ([Weyl 1925]). There is already an excellent account on this and later work of Hermann Weyl on representation theory by Armand Borel ([Borel 1986]) which deals with almost all the strands that came together in Weyl's papers. Also there is forthcoming work by Thomas Hawkins on Weyl's shift of interest from relativity theory to representation theory ([Hawkins 1996]). The aim of this note is to pick up one of these strands leading form the works of A. Hurwitz ([Hurwitz 1897]) and I. Schur ([Schur 1924, I, II, III]) to Weyl's celebrated 'character formula'. These notes arose out of answers to questions by my colleagues at Hamburg University on the meaning and origin of Weyl's denominator identity' (December 1995) and they were successively expanded at the occasion of talks given at the universities of Wuppertal (July 1996), Cordoba (Argentina, August 1996) and Goettingen (January 1997). In these notes we shall adhere to actual mathematical terminology (the talks were addressed to audiences of mathematicians) and we have not made any research into sources beyond published mathematical articles. Thus, from the historical side our presentation may well leave open numerous questions. (orig.)Available from TIB Hannover: RR 9398(72) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman