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arXiv · 1112.2148

The Chern-Connes Character for pseudodifferential operators on the sphere

David P. Dias·Severino T. Melo
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Abstract

We compute the Chern-Connes character (a map from the $K$-theory of a C$^*$-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 ${\rm SO}(3)$. We show that its image is $\mathbb{R}$ if the trace is the integral of the principal symbol.

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David P. Dias, Severino T. Melo. 2011-12-09. The Chern-Connes Character for pseudodifferential operators on the sphere. https://arxiv.org/abs/1112.2148

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