The Crossed Product by a Partial Endomorphism and the Covariance Algebra

الأصل · EN

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 Lρwhich may occur for:C(X) -> C(U) given by (f)=fσ. We obtain examples of partial dynamical systems (Xₐ,σₐ) such that the construction of the covariance algebra C*(Xₐ,σₐ) and the crossed product by partial endomorphism O(Xₐ,,L) associated to this system are not equivalent, in the sense that there does not exists invertible function ρin C(U) such that O(Xₐ,,Lρ)=C*(Xₐ,σ).