Centralizers of finite subgroups of automorphisms and outer automorphisms of free groups /

Thesis (Ph. D.)--Cornell University, August, 1998.

Centralizers of normal subgroups and the Z*-theorem

Peer reviewed

Centralizers of normal subgroups and the Z*-theorem

Peer reviewed

Centralizers of normal subgroups and the Z*-theorem

Peer reviewed

Similarity of Matrices Over Local Rings of Length Two

Let R be a (commutative) local principal ideal ring of length two, for example, the ring R = Z/p(2)Z with p prime. In this paper, we develop a theory of normal forms for similarity classes in the matrix rings M-n (R) by interpreting them in terms of extensions of R t]-modules. Using this theory, we describe the similarity classes in M-n (R) for n <= 4, along with their centralizers. Among these, we characterize those classes which are similar to their transposes. Non-self-transpose classes are shown to exist for all n > 3. When R has finite residue field of order q, we enumerate the similarity classes and the cardinalities of their centralizers as polynomials in q. Surprisingly, the polynomials representing the number of similarity classes in M-n (R) turn out to have non-negative integer coefficients.

Brisure de symétrie par la réduction des groupes de Lie simples à leurs sous-groupes de Lie réductifs maximaux

Dans ce travail, nous exploitons des propriétés déjà connues pour les systèmes de poids des représentations afin de les définir pour les orbites des groupes de Weyl des algèbres de Lie simples, traitées individuellement, et nous étendons certaines de ces propriétés aux orbites des groupes de Coxeter non cristallographiques. D'abord, nous considérons les points d'une orbite d'un groupe de Coxeter fini G comme les sommets d'un polytope (G-polytope) centré à l'origine d'un espace euclidien réel à n dimensions. Nous introduisons les produits et les puissances symétrisées de G-polytopes et nous en décrivons la décomposition en des sommes de G-polytopes. Plusieurs invariants des G-polytopes sont présentés. Ensuite, les orbites des groupes de Weyl des algèbres de Lie simples de tous types sont réduites en l'union d'orbites des groupes de Weyl des sous-algèbres réductives maximales de l'algèbre. Nous listons les matrices qui transforment les points des orbites de l'algèbre en des points des orbites des sous-algèbres pour tous les cas n<=8 ainsi que pour plusieurs séries infinies des paires d'algèbre-sous-algèbre. De nombreux exemples de règles de branchement sont présentés. Finalement, nous fournissons une nouvelle description, uniforme et complète, des centralisateurs des sous-groupes réguliers maximaux des groupes de Lie simples de tous types et de tous rangs. Nous présentons des formules explicites pour l'action de tels centralisateurs sur les représentations irréductibles des algèbres de Lie simples et montrons qu'elles peuvent être utilisées dans le calcul des règles de branchement impliquant ces sous-algèbres.

Mudanças nos modelos de gestão: a política educacional e dos (des)acertos da experiência no Rio Grande do Norte (1995-1999)

This work focuses on the educational policies, on the necessity of adopting new models of administration of the education, as well as the implementation of reforms in this filed during the 1990 s. It analyzes the strategies of decentralization of the education in Rio Grande do Norte, disclosing practices conceived in the governmental plans and programs. It also aims to evidence the aspects of the decentralization proposed in the educational system management model, adopted by the Department of Education and Culture of Rio Grande do Norte from 1995 to 1999. Bibliographic researches and documental analysis were used as sources and semi-structured interviews were held in order to collect data. This work also highlights the concepts of participation, autonomy and democratic management intrinsic to the process of decentralization in the education field. It is clear that decentralization, as the vector of democracy, requires not only certain conditions that assure the universal access to the necessary information, but also that all segments of the institution have a voice in the collegiates and that the management and decision-making processes be transparent. This analysis reveals the importance of creating means to promote autonomy, participation and democratic management in order to consolidate a decentralized system. It is also clear that these mechanisms have been proposed in a vague way by the governmental guidelines, which makes it harder to consolidate a democratic management model. Having this perspective as a parameter, it is possible to realize that the adoption of a management model prompted by the law hasn t established effective means of participation that, consequently, should provide decision centralizers which opposed to the democratic actions

Polynomial and Poisson dependence in free Poisson algebras and free Poisson fields

We prove that any two Poisson dependent elements in a free Poisson algebra and a free Poisson field of characteristic zero are algebraically dependent, thus answering positively a question from Makar-Limanov and Umirbaev (2007) [8]. We apply this result to give a new proof of the tameness of automorphisms for free Poisson algebras of rank two (see Makar-Limanov and Umirbaev (2011) [9], Makar-Limanov et al. (2009) [10]). (C) 2011 Elsevier Inc. All rights reserved.

Examples Illustrating some Aspects of the Weak Deligne-Simpson Problem

Research partially supported by INTAS grant 97-1644