Doctoral Thesis
DOI
10.11606/T.45.2008.tde-05082008-164858
Document
Author
Full name
David Pires Dias
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2008
Supervisor
Committee
Melo, Severino Toscano do Rego (President)
Bianconi, Ricardo
Fernandez, Carlos Eduardo Duran
Silva, Antonio Roberto da
Title in Portuguese
O caráter de Chern-Connes para C*-sistemas dinâmicos calculado em algumas álgebras de operadores pseudodiferenciais
Keywords in Portuguese
Caráter de Chern-Connes
Geometria não-comutativa
Abstract in Portuguese
Dado um C$^*$-sistema dinâmico $(A, G, \alpha)$ define-se um homomorfismo, denominado de caráter de Chern-Connes, que leva elementos de $K_0(A) \oplus K_1(A)$, grupos de K-teoria da C$^*$-álgebra $A$, em $H_{\mathbb}^*(G)$, anel da cohomologia real de deRham do grupo de Lie $G$. Utilizando essa definição, nós calculamos explicitamente esse homomorfismo para os exemplos $(\overline{\Psi_^0(S^1)}, S^1, \alpha)$ e $(\overline{\Psi_^0(S^2)}, SO(3), \alpha)$, onde $\overline{\Psi_^0(M)}$ denota a C$^*$-álgebra gerada pelos operadores pseudodiferenciais clássicos de ordem zero da variedade $M$ e $\alpha$ a ação de conjugação pela representação regular (translações).
Title in English
The C*-dynamical system Chern-Connes character computed in some pseudodifferential operators algebras
Keywords in English
C*-algebras generated by pseudodifferential operators.
Chern-Connes character
Noncommutative Geometry
Abstract in English
Given a C$^*$-dynamical system $(A, G, \alpha)$ one defines a homomorphism, called the Chern-Connes character, that take an element in $K_0(A) \oplus K_1(A)$, the K-theory groups of the C$^*$-algebra $A$, and maps it into $H_{\mathbb}^*(G)$, the real deRham cohomology ring of $G$. We explictly compute this homomorphism for the examples $(\overline{\Psi_^0(S^1)}, S^1, \alpha)$ and $(\overline{\Psi_^0(S^2)}, SO(3), \alpha)$, where $\overline{\Psi_^0(M)}$ denotes the C$^*$-álgebra gene\-rated by the classical pseudodifferential operators of zero order in the manifold $M$ and $\alpha$ the action of conjugation by the regular representation (translations).