A residue formula for the fundamental Hochschild 3-cocycle for \(SU_{q}(2)\) (Q2892869)
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scientific article; zbMATH DE number 6049467
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A residue formula for the fundamental Hochschild 3-cocycle for \(SU_{q}(2)\) |
scientific article; zbMATH DE number 6049467 |
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25 June 2012
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spectral triples
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Dirac operators
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cyclic cohomology
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quantum groups
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quantum SU(2)
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residue formulas
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Calabi-Yau algebras
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math.OA
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math.QA
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A residue formula for the fundamental Hochschild 3-cocycle for \(SU_{q}(2)\) (English)
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To describe the geometry of quantum groups and their homogeneous spaces requires that we generalise the axioms for noncommutative smooth manifolds and spectral triples. Several generalisations have been suggested in recent years. This article works out another example and constructs a variant of a spectral triple over the quantum group SU\(_q(2)\). This is not a spectral triple because the crucial axiom about bounded commutators \([D,a]\) is violated. Nevertheless, the authors manage in a somewhat ad hoc way to associate a twisted Hochschild 3-cocycle to this situation. This turns out to be the standard twisted 3-cocycle on SU\(_q(2)\). Besides the usual data used in a spectral triple, they also cut operators down with certain projections to get finite results.
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