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• W1579125172 abstract "We formulate and prove an extension of Connes’s reconstruction theorem for commutative spectral triples to so-called Connes–Landi or isospectral deformations of commutative spectral triples along the action of a compact Abelian Lie group G, also known as toric noncommutative manifolds. In particular, we propose an abstract definition for such spectral triples, where noncommutativity is entirely governed by a deformation parameter sitting in the second group cohomology of the Pontryagin dual of G, and then show that such spectral triples are well-behaved under further Connes–Landi deformation, thereby allowing for both quantisation from and dequantisation to G-equivariant abstract commutative spectral triples. We then use a refinement of the Connes–Dubois-Violette splitting homomorphism to conclude that suitable Connes–Landi deformations of commutative spectral triples by a rational deformation parameter are almost-commutative in the general, topologically non-trivial sense." @default.
• W1579125172 created "2016-06-24" @default.
• W1579125172 creator A5083576720 @default.
• W1579125172 date "2015-12-01" @default.
• W1579125172 modified "2023-09-25" @default.
• W1579125172 title "A reconstruction theorem for Connes–Landi deformations of commutative spectral triples" @default.
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• W1579125172 doi "https://doi.org/10.1016/j.geomphys.2015.07.028" @default.
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