Quantization of Poisson algebras associated to Lie algebroids

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dc.creatorLandsman, N. P.
dc.creatorRamazan, B.
dc.date2000-01-04
dc.date2000-11-21
dc.date.accessioned2026-07-07T04:27:34Z
dc.date.available2026-07-07T04:27:34Z
dc.descriptionWe prove the existence of a strict deformation quantization for the canonical Poisson structure on the dual of an integrable Lie algebroid. It follows that any Lie groupoid C*-algebra may be regarded as a result of a quantization procedure. The C*-algebra of the tangent groupoid of a given Lie groupoid G (with Lie algebra g) is the C*-algebra of a continuous field of C*-algebras over R with fibers A_0=C*(g)=C_0(g*) and A_h=C*(G) for nonzero h. The same is true for the corresponding reduced C*-algebras. Our results have applications to, e.g., transformation group C*-algebras, K-theory, and index theory.
dc.description34 pages, minor corrections
dc.identifierhttps://arxiv.org/abs/math-ph/0001005
dc.identifierhttp://arxiv.org/abs/math-ph/0001005
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/56461
dc.subjectMathematical Physics
dc.subjectOperator Algebras
dc.subjectQuantum Algebra
dc.subjectSymplectic Geometry
dc.subject46L65; 81S99
dc.titleQuantization of Poisson algebras associated to Lie algebroids
dc.typetext

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