New York Journal of Mathematics
Volume 22 (2016) 1139-1220


Jeffrey L. Boersema and Terry A. Loring

K-theory for real C*-algebras via unitary elements with symmetries

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Published: September 30, 2016
Keywords: topological insulator, semiprojectivity, K-theory, E-theory, ten-fold way
Subject: 46L80, 19K99, 81Q99

We prove that all eight KO groups for a real C*-algebra can be constructed from homotopy classes of unitary matrices that respect a variety of symmetries. In this manifestation of the KO groups, all eight boudary maps in the 24-term exact sequences associated to an ideal in a real C*-algebra can be computed as exponential or index maps with formulas that are nearly identical to the complex case.


This work was partially supported by a grant from the Simons Foundation (208723 to Loring).

Author information

Jeffrey L. Boersema:
Seattle University, Department of Mathematics, Seattle, Washington 98133, USA

Terry A. Loring:
University of New Mexico, Department of Mathematics and Statistics, Albuquerque, New Mexico 87131, USA