Entire cyclic homology of Schatten ideals

2004/09/09 by Jacek Brodzki, J. Brodzki, Brodzki, J. +3
Mathematics · #19D55 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Holomorphic and Operator Theory #K-Theory and Homology (math.KT) #math.KT #msc:19D55

paper · pdf · doi:10.48550/arxiv.math/0409164

17 pages, revised introduction and last section

openalex publication_date 2004/09/09 · arxiv created 2004/09/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Certain cocycles constructed by Connes are characters of p-summable Fredholm modules. In this article, we establish some consequences of the universal properties which these characters enjoy. Our main technical result is that the entire cyclic cohomology of the p-th Schatten ideal L^p (respectively, homology) is independent of p and isomorphic to the entire cyclic cohomology (respectively, homology) of the ideal of trace class operators L¹.

Citations

• Analytic cyclic cohomology

Related

• Fredholm modules over categories, Connes periodicity and classes in cyclic cohomology
• Analytic cyclic cohomology
• The asymptotic Connes-Moscovici characteristic map and the index\n cocycles
• Cyclic Theory and the Bivariant Chern-Connes Character
• Hopf-cyclic homology and cohomology with coefficients