O carater de Chern-Connes para C${}^{\ast }$-sistemas dinamicos calculado em algumas algebras de operadores pseudodiferenciais

Abstract

Given a C${}^{\ast }$-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${}^{\ast }$-algebra $A$, and maps it into $H_{\mathbb{R}}^{\ast }(G)$, the real deRham cohomology ring of $G$. We explictly compute this homomorphism for the examples $(\overline{{\Psi }_{cl}^0(S^1)},S^1,\alpha )$ and $(\overline{{\Psi }_{cl}^0(S^2)},SO(3),\alpha )$, where $\overline{{\Psi }_{cl}^0(M)}$ denotes the C${}^{\ast }$-algebra generated by the classical pseudodifferential operators of zero order in the manifold $M$ and $\alpha$ the action of conjugation by the regular representation (translations).

This is a PhD thesis in portuguese supervised by Severino T. Melo