dorsal/arxiv
View SchemaContractions on the Classical Double
| Authors | Angel Ballesteros, Mariano del Olmo |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9702031 |
| URL | https://arxiv.org/abs/q-alg/9702031 |
Abstract
Lie algebra contractions on the classical Drinfel'd Double of a given Lie bialgebra are introduced and compared to the usual Lie bialgebra contraction theory. The connection between both approaches turns out to be intimately linked to duality problems. The non-relativistic (Galilean) limit of a (1+1) Poincar\'e Double is used to illustrate the contraction process. Finally, it is shown that, in a certain sense, the classical limit in a quantum algebra can be thought as a certain contraction on the corresponding Double.
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"abstract": "Lie algebra contractions on the classical Drinfel\u0027d Double of a given Lie\nbialgebra are introduced and compared to the usual Lie bialgebra contraction\ntheory. The connection between both approaches turns out to be intimately\nlinked to duality problems. The non-relativistic (Galilean) limit of a (1+1)\nPoincar\\\u0027e Double is used to illustrate the contraction process. Finally, it is\nshown that, in a certain sense, the classical limit in a quantum algebra can be\nthought as a certain contraction on the corresponding Double.",
"arxiv_id": "q-alg/9702031",
"authors": [
"Angel Ballesteros",
"Mariano del Olmo"
],
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"q-alg",
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"title": "Contractions on the Classical Double",
"url": "https://arxiv.org/abs/q-alg/9702031"
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