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Master's Dissertation
DOI
10.11606/D.55.2018.tde-06032018-084334
Document
Author
Full name
Eliane Zerbetto Traldi
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 1999
Supervisor
Committee
Manzoli Neto, Oziride (President)
Barros, Tomas Edson
Campos, José Eduardo Prado Pires de
Title in Portuguese
Sistemas Aumentados de Grupos e Shifts de Tipo Finito
Keywords in Portuguese
Não disponível
Abstract in Portuguese
Seja (G, X, x) uma terna consistindo de um grupo finitamente apresentado G, um epimorfismo x : G → Z, e um elemento distingüido x ∈ G tal que x(x) = 1. Dado um grupo simétrico, construímos um grafo direcionado finito ⌈ que descreve o conjunto Φr de representações ρ Ker (x) → Sr bem como a aplicação σx : Φr → Φr definida por (σxρ)(a) = ρ(x-1 ax) para todo a ∈ Ker(x). O par (Φr, σx) tem a estrutura de um shift de tipo finito. Discutimos propriedades básicas e aplicações do shift representação (Φr, σx), incluindo aplicações à Teoria de Nós.
Title in English
Not available
Keywords in English
Not available
Abstract in English
Let (G, X, x) be a triple consisting of a finitely presented group G, an epimorphism x: G → Z, and a distinguished element x ∈ G such that X(x) = 1. Given a finite symmetric group Sr, we construct a finite directed graph ⌈ that describes the set of Φr of representations p: Ker(x) → Sr as well as the mapping σx : Φr → Φr defined by (σxρp)(a) = ρ(x-lax) for all a ∈ Ker(x). The pair (Φr, σx) has the structure of a shift of finite type. We discuss basic properties and applications of the representation shift (Φr, σx), including applications to knot theory.
 
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ElianeZerbettoTraldi.pdf (940.30 Kbytes)
Publishing Date
2018-03-09
 
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