FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2007, VOLUME 13, NUMBER 8, PAGES 133-169

Universal Karoubi's characteristic classes of nuclear $C$*-algebras

I. M. Nikonov

Abstract

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The main result of this paper is the evaluation of kernels for the Chern character and the universal Karoubi classes of nuclear $C$*-algebras. It is shown that the kernel of the Chern character coincides with the subgroup of infinitely small elements of the $K$₀-group and the kernel of the universal Karoubi classes coincides with the subgroup of approximately scalar elements of the $K$₀-group.

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Last modified: June 13, 2008