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C*-algebras of commuting endomorphisms

Valentin Deaconu
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Abstract

Given a compact space X and two commuting continuous open surjective maps sigma_1, sigma_2 : X --> X, we construct certain C*-algebras that reflect the dynamics of the N^2-action. When the maps sigma_1, sigma_2 are local homeomorphisms, these are groupoid algebras, but in general, we will use a Cuntz-Pimsner algebra associated to a product system of Hilbert bimodules in the sense of Fowler. The motivating example for our construction is the dynamical system associated with a rank two graph by Kumjian and Pask. We consider also a two-dimensional subshift of Ledrappier, the case of two covering maps of the circle, and the two-dimensional Bernoulli shift.

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Valentin Deaconu. 2004-06-30. C*-algebras of commuting endomorphisms. https://arxiv.org/abs/math/0406624

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