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- W3103231735 abstract "While there has been growing interest for noncommutative spaces in recent times, most examples have been based on the simplest noncommutative algebra: [x_i,x_j]=i theta_{ij}. Here we present new classes of (non-formal) deformed products associated to linear Lie algebras of the kind [x_i,x_j]=ic_{ij}^k x_k. For all possible three-dimensional cases, we define a new star product and discuss its properties. To complete the analysis of these novel noncommutative spaces, we introduce noncompact spectral triples, and the concept of star triple, a specialization of the spectral triple to deformations of the algebra of functions on a noncompact manifold. We examine the generalization to the noncompact case of Connes' conditions for noncommutative spin geometries, and, in the framework of the new star products, we exhibit some candidates for a Dirac operator. On the technical level, properties of the Moyal multiplier algebra M(R_theta^{2n) are elucidated." @default.
- W3103231735 created "2020-11-23" @default.
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- W3103231735 date "2002-04-16" @default.
- W3103231735 modified "2023-10-17" @default.
- W3103231735 title "Infinitely many star products to play with" @default.
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- W3103231735 doi "https://doi.org/10.1088/1126-6708/2002/04/026" @default.
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