The Chern-Connes Character for pseudodifferential operators on the sphere

Abstract

We compute the Chern-Connes character (a map from the $K$-theory of a C${}^{\ast }$-algebra under the action of a Lie group to the cohomology of its Lie algebra) for the $L^2$-norm closure of the algebra of all classical zero-order pseudodifferential operators on the sphere under the canonical action of $\mathrm{SO}(3)$. We show that its image is $\mathbb{R}$ if the trace is the integral of the principal symbol.

References in corpus (1)

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