A note on Q-algebra and quantization

Details A note on Q-algebra and quantization A note on Q-algebra and quantization

2005-08-17

arxiv.org/abs/math-ph/0508035v2

Physics

Mathematical Physics

13 pages

Scientific paper

10.1007/s11005-005-0046-2

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 K\"ahler manifold. In particular, we relate this construction on $\complex\mathbb{P}^1$ to representations of a fuzzy sphere.

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