Unit spectra of Ktheory from strongly selfabsorbing C*algebras
Abstract
We give an operator algebraic model for the first group of the unit spectrum $gl_1(KU)$ of complex topological Ktheory, i.e. $[X, BGL_1(KU)]$, by bundles of stabilized infinite Cuntz C*algebras $O_{\infty} \otimes \K$. We develop similar models for the localizations of $KU$ at a prime $p$ and away from $p$. Our work is based on the $\mathcal{I}$monoid model for the units of $K$theory by Sagave and Schlichtkrull and it was motivated by the goal of finding connections between the infinite loop space structure of the classifying space of the automorphism group of stabilized strongly selfabsorbing C*algebras that arose in our generalization of the DixmierDouady theory and classical spectra from algebraic topology.
 Publication:

arXiv eprints
 Pub Date:
 June 2013
 DOI:
 10.48550/arXiv.1306.2583
 arXiv:
 arXiv:1306.2583
 Bibcode:
 2013arXiv1306.2583D
 Keywords:

 Mathematics  Algebraic Topology;
 Mathematics  KTheory and Homology;
 Mathematics  Operator Algebras;
 55N15 55P42 46L80
 EPrint:
 25 pages