Quantization of branched coverings
| Autor: | A. A. Pavlov, E. V. Troitskii |
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| Rok vydání: | 2011 |
| Předmět: |
Pure mathematics
Quantization (signal processing) Unital General Topology (math.GN) Mathematics - Operator Algebras Hausdorff space Geometric Topology (math.GT) Statistical and Nonlinear Physics Conditional expectation Noncommutative geometry 46L08 (Primary) 46L85 55R55 (Secondary) Mathematics - Geometric Topology FOS: Mathematics Finitely-generated abelian group Operator Algebras (math.OA) Bijection injection and surjection Mathematical Physics Mathematics - General Topology Mathematics |
| Zdroj: | Russian Journal of Mathematical Physics. 18:338-352 |
| ISSN: | 1555-6638 1061-9208 |
| DOI: | 10.1134/s1061920811030071 |
| Popis: | We identify branched coverings (continuous open surjections p:Y->X of Hausdorff spaces with uniformly bounded number of pre-images) with Hilbert C*-modules C(Y) over C(X) and with faithful unital positive conditional expectations E:C(Y)->C(X) topologically of index-finite type. The case of non-branched coverings corresponds to projective finitely generated modules and expectations (algebraically) of index-finite type. This allows to define non-commutative analogues of (branched) coverings. v2:Small changes in examples and references. Submitted. |
| Databáze: | OpenAIRE |
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