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Correction for Fox, Int Math Res Papers 2005 461-510.
International Mathematics Research Papers (2005) 2005:461-510, doi:10.1155/IMRP.2005.461
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Copyright © 2005 Hindawi Publishing Corporation. All rights reserved.

Projectively invariant star products

Daniel J. F. Fox

It is shown that a (curved) projective structure on a smooth manifold determines on the Poisson algebra of smooth functions on the cotangent bundle, fiberwise-polynomial of bounded degree, a one-parameter family of graded star products. For a particular value of the parameter (corresponding to half-densities), the star product is symmetric and specializes in the projectively flat case to the one constructed previously by C. Duval, P. Lecomte, and V. Ovsienko. These star products are built from a projectively invariant quantization map associating to a symmetric polyvector a formally selfadjoint operator on densities. A limiting form of this family of star products yields a commutative deformation of the symmetric tensor algebra of the manifold which is closely related to the limiting commutative multiplication of modular forms defined by P. Cohen, Y. Manin, and D. Zagier. A basic ingredient of the proof is the construction of projectively invariant multilinear differential operators on bundles of weighted symmetric k-vectors. The construction works except for a discrete set of excluded weights and generalizes the Rankin-Cohen brackets of modular forms.

Erratum "Projectively invariant star products" dx.doi.org/10.1155/IMRP/2006/93234


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Erratum to "Projectively invariant star products"
Int Math Res Papers, January 1, 2006; 2006(O93234): 93234 - 3.
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