dorsal/arxiv
View SchemaHochschild cohomology and characteristic classes for star-products
| Authors | Alan Weinstein, Ping Xu |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9709043 |
| URL | https://arxiv.org/abs/q-alg/9709043 |
Abstract
We show that the Hochschild cohomology of the algebra obtained by formal deformation quantization on a symplectic manifold is isomorphic to the formal series with coefficients in the de Rham cohomology of the manifold. The cohomology class obtained by differentiating the star-product with respect to the deformation parameter is seen to be closely related to the characteristic class of the quantization. A fundamental role in the analysis is played by ``quantum Liouville operators,'' which rescale the deformation parameter in the same way in which Liouville vector fields scale the Poisson structure (or the units of action). Several examples are given.
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"abstract": "We show that the Hochschild cohomology of the algebra obtained by formal\ndeformation quantization on a symplectic manifold is isomorphic to the formal\nseries with coefficients in the de Rham cohomology of the manifold. The\ncohomology class obtained by differentiating the star-product with respect to\nthe deformation parameter is seen to be closely related to the characteristic\nclass of the quantization. A fundamental role in the analysis is played by\n``quantum Liouville operators,\u0027\u0027 which rescale the deformation parameter in the\nsame way in which Liouville vector fields scale the Poisson structure (or the\nunits of action). Several examples are given.",
"arxiv_id": "q-alg/9709043",
"authors": [
"Alan Weinstein",
"Ping Xu"
],
"categories": [
"q-alg",
"dg-ga",
"math.DG",
"math.QA"
],
"title": "Hochschild cohomology and characteristic classes for star-products",
"url": "https://arxiv.org/abs/q-alg/9709043"
},
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