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An inductive explicit construction of $*$-products on some Poisson manifolds


Author: Santos Asin Lares
Journal: Proc. Amer. Math. Soc. 128 (2000), 1853-1857
MSC (1991): Primary 58F06, 53Z05; Secondary 81Q99.
DOI: https://doi.org/10.1090/S0002-9939-99-05250-8
Published electronically: September 30, 1999
MathSciNet review: 1654089
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Abstract: We extend the Cahen Gutt coboundary construction on cotangent bundles of $n$-dimensional parallelisable manifolds to manifolds which admit $n$ global vector fields defining a parallelisation on a dense open set. This result is used to give an inductive explicit construction of $*$-products on certain Poisson manifolds.


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Additional Information

Santos Asin Lares
Affiliation: Mathematical Institute, University of Warwick, CV4-7AL, United Kingdom
Email: asin@maths.warwick.ac.uk

DOI: https://doi.org/10.1090/S0002-9939-99-05250-8
Keywords: $*$-product, deformation quantization
Received by editor(s): July 21, 1998
Published electronically: September 30, 1999
Additional Notes: The author was supported by a grant from the University of Warwick.
Communicated by: Peter Li
Article copyright: © Copyright 2000 American Mathematical Society

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