The Chern-Connes Character for pseudodifferential operators on the sphere

2011/12/09 by Dias, David P., Melo, Severino T.
#46L80 (47G30 #58B34) #FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1112.2148

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 L²-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 ℝ if the trace is the integral of the principal symbol.

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