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Pré-Publication, Document De Travail Année : 2006

An algebra of deformation quantization for star-exponentials on complex symplectic manifolds

Giuseppe Dito
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  • PersonId : 829179
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Pierre Schapira
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  • PersonId : 834249

Résumé

The cotangent bundle $T^*X$ to a complex manifold $X$ is classically endowed with the sheaf of $\cor$-algebras $\W[T^*X]$ of deformation quantization, where $\cor\eqdot \W[\rmptt]$ is a subfield of $\C[[\hbar,\opb{\hbar}]$. Here, we construct a new sheaf of $\cor$-algebras $\TW[T^*X]$ which contains $\W[T^*X]$ as a subalgebra and an extra central parameter $t$. We give the symbol calculus for this algebra and prove that quantized symplectic transformations operate on it. If $P$ is any section of order zero of $\W[T^*X]$, we show that $\exp(t\opb{\hbar} P)$ is well defined in $\TW[T^*X]$.
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Dates et versions

hal-00084660 , version 1 (10-07-2006)

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Giuseppe Dito, Pierre Schapira. An algebra of deformation quantization for star-exponentials on complex symplectic manifolds. 2006. ⟨hal-00084660⟩
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