• JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
 
  Bookmark and Share
 
 
Master's Dissertation
DOI
https://doi.org/10.11606/D.45.2011.tde-15052011-173459
Document
Author
Full name
Priscilla Iastremski
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2011
Supervisor
Committee
Cerri, Cristina (President)
Melo, Severino Toscano do Rego
Vicens, Fernando Raul Abadie
Title in Portuguese
O produto cruzado de uma C*-álgebra por um endomorfismo e a álgebra de Cuntz-Krieger
Keywords in Portuguese
C*-álgebras
Cuntz-Krieger
Produto-cruzado
Abstract in Portuguese
Dados A uma C*-álgebra com unidade e \alpha um *-endomorfismo de A, um operador transferência para o par (A, \alpha) é uma aplicação linear contínua positiva L: A --> A tal que L(\alpha(a)b) = a L(b), para todo a, b \in A. Nestas condições, denotamos por T(A, \alpha, L) a C*-álgebra universal com unidade gerada por A e um elemento S sujeito às relações Sa = \alpha(a)S e S*aS = L(a). Uma redundância é definida como o par (a, k) \in A x \overline{ASS* A} tal que abS = akS, para todo b \in A. Neste trabalho definimos a C*-álgebra chamada de produto cruzado como o quociente de T(A, \alpha, L) pelo ideal bilateral fechado I gerado pelo conjunto das diferenças a-k, para todas as redundâncias (a, k) tais que a \in \overline, onde R denota a Im \alpha. Mostramos que quando \alpha é injetor com imagem hereditária, então o produto cruzado é isomorfo à C*-álgebra universal com unidade, denotada por U(A, \alpha), gerada por A e uma isometria T sujeita à relação \alpha(a) = TaT*, para todo a \in A. Também mostramos que a álgebra de Cuntz-Krieger O_A pode ser caracterizada como o produto cruzado definido neste trabalho.
Title in English
The crossed-product of a C*-algebra by an endomorphism and the Cuntz-Krieger algebra
Keywords in English
C*-algebra
Crossed-product
Cuntz-Krieger
Abstract in English
Given A a C*-algebra with unit and \alpha an *-endomorphism of A, a transfer operator for the pair (A, \alpha) is a continuous positive linear map L: A --> A such that L(\alpha(a)b) = a L(b), for all a, b \in A. Under these conditions , we denote by T(A, \alpha, L) the universal C*-algebra with unit generated by A and an element S subject to the relations Sa = \alpha(a)S and S*aS = L(a). A redundancy is defined as a pair (a, k) \in A x \overline{ASS* A} such that abS = akS, for all b \in A. In tjis work we define the C*-algebra called crossed-product as the quotient of T(A, \alpha, L) by the closed two-sided ideal I generated by the set of all differences a-k, for all redundancies (a, k) such that a \in \overline, where by R we mean Im \alpha. We prove that when \alpha is injective with an hereditary range, then the crossed-product is isomorphic to the universal C*-algebra with unit, which we denote by U(A, \alpha), generated by A and an isometry T subject to the relation \alpha(a) = TaT*, for all a \in A. We also prove that the Cuntz-Krieger algebra O_A can be characterized as the crossed-product we define in this work.
 
WARNING - Viewing this document is conditioned on your acceptance of the following terms of use:
This document is only for private use for research and teaching activities. Reproduction for commercial use is forbidden. This rights cover the whole data about this document as well as its contents. Any uses or copies of this document in whole or in part must include the author's name.
dissertacao.pdf (350.61 Kbytes)
Publishing Date
2011-06-07
 
WARNING: Learn what derived works are clicking here.
All rights of the thesis/dissertation are from the authors
CeTI-SC/STI
Digital Library of Theses and Dissertations of USP. Copyright © 2001-2024. All rights reserved.