A (holomorphic) quantization of a complex contact manifold is given by an $\she$-algebroid, i.e. a stack locally equivalent to the ring of microdifferential operators. The existence of a canonical quantization has been proved by Kashiwara. In this paper we first consider the classification problem, showing that the $\she$-algebroids are classified by means of a certain homogeneous deRham complex. Second, we consider the problem of existence and classification for (formal) $\she$-algebras.
Quantization of complex contact manifolds
POLESELLO, PIETRO
2012
Abstract
A (holomorphic) quantization of a complex contact manifold is given by an $\she$-algebroid, i.e. a stack locally equivalent to the ring of microdifferential operators. The existence of a canonical quantization has been proved by Kashiwara. In this paper we first consider the classification problem, showing that the $\she$-algebroids are classified by means of a certain homogeneous deRham complex. Second, we consider the problem of existence and classification for (formal) $\she$-algebras.
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