Title: $C*$-algebras generated by groups of composition operators

Authors: Michael Jury

Issue: Volume 56 (2007), Issue 6, 3171-3192

Abstract: We compute the C*-algebra generated by a group of composition operators acting on certain reproducing kernel Hilbert spaces over the disk, where the symbols belong to a non-elementary Fuchsian group. We show that such a C*-algebra contains the compact operators, and its quotient is isomorphic to the crossed product C*-algebra determined by the action of the group on the boundary circle. In addition we show that the C*-algebras obtained from composition operators acting on a natural family of Hilbert spaces are in fact isomorphic, and also determine the same Ext-class, which can be related to known extensions of the crossed product.