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

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