Pseudo-differential Operators and Regularity of Spectral Triples
classification
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math.KT
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operatorspseudo-differentialregularspectralalgebrageneralizedtriplesadmits
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We introduce a notion of an algebra of generalized pseudo-differential operators and prove that a spectral triple is regular if and only if it admits an algebra of generalized pseudo-differential operators. We also provide a self-contained proof of the fact that the product of regular spectral triples is regular.
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