O carater de Chern-Connes para C$^*$-sistemas dinamicos calculado em algumas algebras de operadores pseudodiferenciais

Details O carater de Chern-Connes para C$^*$-sistemas dinamicos calculado em algumas algebras de operadores pseudodiferenciais O carater de Chern-Connes para C$^*$-sistemas dinamicos calculado em algumas algebras de operadores pseudodiferenciais

2008-08-04

arxiv.org/abs/0808.0512v1

Mathematics

Operator Algebras

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

Scientific paper

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 $H_{\mathbb{R}}^*(G)$, 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$^*$-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).

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