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The Crossed Product by a Partial Endomorphism and the Covariance Algebra

Danilo Royer
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Abstract

Given a local homeomorphism σ:U -> X where U is a clopen subset of an compact and Hausdorff topological space X, we obtain the possible transfer operators L_ρwhich may occur for \al:C(X) -> C(U) given by \al(f)=fσ. We obtain examples of partial dynamical systems (X_A,σ_A) such that the construction of the covariance algebra C^*(X_A,σ_A) and the crossed product by partial endomorphism O(X_A,\al,L) associated to this system are not equivalent, in the sense that there does not exists invertible function ρin C(U) such that O(X_A,\al,L_ρ)=C^*(X_A,σ).

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Danilo Royer. 2005-03-21. The Crossed Product by a Partial Endomorphism and the Covariance Algebra. https://arxiv.org/abs/math/0503439

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