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A note on Q-algebra and quantization

Xiang Tang
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Abstract

In this note, we study Schwarz's conjecture on application of Q-algebras to strict quantization. We prove that in the case of a torus with a constant Poisson structure, Schwarz's formalism gives the same star product as Rieffel \cite{rif:quantization}. We construct twisted Fock modules as examples of quantization dg-modules in the case of a compact Kähler manifold. In particular, we relate this construction on $\complex\mathbb{P}^1$ to representations of a fuzzy sphere.

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Xiang Tang. 2005-11-06. A note on Q-algebra and quantization. https://doi.org/10.1007/s11005-005-0046-2

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