dorsal/arxiv
View SchemaQuantum groupoids and deformation quantization
| Authors | Ping Xu |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9708020 |
| URL | https://arxiv.org/abs/q-alg/9708020 |
| DOI | 10.1016/S0764-4442(97)82982-5 |
Abstract
The purpose of this Note is to unify quantum groups and star-products under a general umbrella: quantum groupoids. It is shown that a quantum groupoid naturally gives rise to a Lie bialgebroid as a classical limit. The converse question, i.e., the quantization problem, is posed. In particular, any regular triangular Lie bialgebroid is shown quantizable. For the Lie bialgebroid of a Poisson manifold, its quantization is equivalent to a star-product.
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"abstract": "The purpose of this Note is to unify quantum groups and star-products under a\ngeneral umbrella: quantum groupoids. It is shown that a quantum groupoid\nnaturally gives rise to a Lie bialgebroid as a classical limit. The converse\nquestion, i.e., the quantization problem, is posed. In particular, any regular\ntriangular Lie bialgebroid is shown quantizable. For the Lie bialgebroid of a\nPoisson manifold, its quantization is equivalent to a star-product.",
"arxiv_id": "q-alg/9708020",
"authors": [
"Ping Xu"
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"doi": "10.1016/S0764-4442(97)82982-5",
"title": "Quantum groupoids and deformation quantization",
"url": "https://arxiv.org/abs/q-alg/9708020"
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