Existence of natural and projectively equivariant quantizations

• Autores: Sarah Hansoul
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 214, Nº 2, 2007, págs. 832-864
• Idioma: inglés
• DOI: 10.1016/j.aim.2007.03.007
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• Resumen

  • We study the existence of natural and projectively equivariant quantizations for differential operators acting between order 1 vector bundles over a smooth manifold M. To that aim, we make use of the Thomas¿Whitehead approach of projective structures and construct a Casimir operator depending on a projective Cartan connection. We attach a scalar parameter to every space of differential operators, and prove the existence of a quantization except when this parameter belongs to a discrete set of resonant values.