Journal of Operator Theory

Volume 62, Issue 1, Summer 2009 pp. 159-169.

The

$C^*$ -algebra of symmetric words in two universal unitaries

Authors: Man-Duen Choi (1) and Frederic Latremoliere
Author institution: (1) Department of Mathematics, University of Toronto, Toronto, M5S 2E4, Canada
(2) Department of Mathematics, University of Denver, Denver, 80208, U.S.A.

Summary: We compute the

$K$ -theory of the

$C^*$ -algebra of symmetric words in two universal unitaries. This algebra is the fixed point

$C^*$ -algebra for the order-two automorphism of the full

$C^*$ -algebra of the free group on two generators which switches the generators. Our calculations relate the

$K$ -theory of this

$C^*$ -algebra to the

$K$ -theory of the associated

$C^*$ -crossed-product by

$\mathbb{Z}_{2}$ .

Contents Full-Text PDF