dorsal/arxiv
View SchemaOn the existence of deformed Lie-Poisson structures for quantized groups
| Authors | V. D. Lyakhovsky, A. M. Mirolubov |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9606013 |
| URL | https://arxiv.org/abs/q-alg/9606013 |
| DOI | 10.1023/A:1021496128802 |
Abstract
The geometrical description of deformation quantization based on quantum duality principle makes it possible to introduce deformed Lie-Poisson structure. It serves as a natural analogue of classical Lie bialgebra for the case when the initial object is a quantized group. The explicit realization of the deformed Lie-Poisson structure is a difficult problem. We study the special class of such constructions characterized by quite a simple form of tanjent vector fields. It is proved that in such a case it is sufficient to find four Lie compositions that form two deformations of the first order and four Lie bialgebras. This garantees the existence of two families of deformed Lie-Poisson structures due to the intrinsic symmetry of the initial compositions. The explicit example is presented.
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"abstract": "The geometrical description of deformation quantization based on quantum\nduality principle makes it possible to introduce deformed Lie-Poisson\nstructure. It serves as a natural analogue of classical Lie bialgebra for the\ncase when the initial object is a quantized group. The explicit realization of\nthe deformed Lie-Poisson structure is a difficult problem. We study the special\nclass of such constructions characterized by quite a simple form of tanjent\nvector fields. It is proved that in such a case it is sufficient to find four\nLie compositions that form two deformations of the first order and four Lie\nbialgebras. This garantees the existence of two families of deformed\nLie-Poisson structures due to the intrinsic symmetry of the initial\ncompositions. The explicit example is presented.",
"arxiv_id": "q-alg/9606013",
"authors": [
"V. D. Lyakhovsky",
"A. M. Mirolubov"
],
"categories": [
"q-alg",
"math.QA"
],
"doi": "10.1023/A:1021496128802",
"title": "On the existence of deformed Lie-Poisson structures for quantized groups",
"url": "https://arxiv.org/abs/q-alg/9606013"
},
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