C*-algebras of Penrose's hyperbolic tilings
Operator Algebras
2010-06-09 v2 Dynamical Systems
Abstract
Penrose hyperbolic tilings are tilings of the hyperbolic plane which admit, up to affine transformations a finite number of prototiles. In this paper, we give a complete description of the C*-algebras and of the K-theory for such tilings. Since the continuous hull of these tilings have no transversally invariant measure, these C*-algebras are traceless. Nevertheless, harmonic currents give rise to 3-cyclic cocycles and we discuss in this setting a higher-order version of the gap-labelling.
Keywords
Cite
@article{arxiv.0905.1932,
title = {C*-algebras of Penrose's hyperbolic tilings},
author = {Hervé Oyono-Oyono and Samuel Petite},
journal= {arXiv preprint arXiv:0905.1932},
year = {2010}
}
Comments
36 pages. v2: some mistakes corrected, a section on topological invariants of the continuous hull of the Penrose hyperbolic tilings added