Journal of Operator Theory

Volume 93, Issue 2, Spring 2025 pp. 413-434.

Polar decomposition in algebraic K-theory

Authors: Pawel Sarkowicz (1), Aaron Tikuisis (2)
Author institution: (1) Department of Pure Mathematics, University of Waterloo, Waterloo, N2L 3G1, Canada
(2) Department of Mathematics and Statistics, University of Ottawa, Ottawa, K1N 6N5, Canada

Summary: We show that the Hausdorffized algebraic K-theory of a unital $C^*$-algebra decomposes naturally as a direct sum of the Hausdorffized unitary algebraic K-theory and the space of continuous affine functions on the trace simplex. Under mild regularity hypotheses, an analogous natural direct sum decomposition holds for the ordinary (non-Hausdorffized) algebraic K-theory.

DOI: http://dx.doi.org/10.7900/jot.2023may29.2436
Keywords: $C^*$-algebras, K-theory, nonstable K-theory, algebraic K-theory

Contents Full-Text PDF