The crossed product by a partial endomorphism and the covariance algebra |
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Authors: | Danilo Royer |
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Affiliation: | Departamento de Matemática, Universidade Federal de Santa Catarina, 88040-900, Florianópolis SC, Brazil |
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Abstract: | Given a local homeomorphism where U⊆X is clopen and X is a compact and Hausdorff topological space, we obtain the possible transfer operators Lρ which may occur for given by α(f)=f○σ. We obtain examples of partial dynamical systems (XA,σA) such that the construction of the covariance algebra C∗(XA,σA), proposed by B.K. Kwasniewski, and the crossed product by a partial endomorphism O(XA,α,L), recently introduced by the author and R. Exel, associated to this system are not equivalent, in the sense that there does not exist an invertible function ρ∈C(U) such that O(XA,α,Lρ)≅C∗(XA,σA). |
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Keywords: | Partial endomorphism Crossed product Covariance algebra |
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