dorsal/arxiv
View SchemaClassical Limits, Quantum Duality and Lie-Poisson Structures
| Authors | V. D. Lyakhovsky |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9506025 |
| URL | https://arxiv.org/abs/q-alg/9506025 |
Abstract
Quantum duality principle is applied to study classical limits of quantum algebras and groups. For a certain type of Hopf algebras the explicit procedure to construct both classical limits is presented. The canonical forms of quantized Lie-bialgebras are proved to be two-parametric varieties with two classical limits called dual. When considered from the point of view of quantized symmetries such varieties can have boundaries that are noncommutative and noncocommutative. In this case the quantum duality and dual limits still exist while instead of Lie bialgebra one has a pair of tangent vector fields. The properties of these constructions called quantizations of Hopf pairs are studied and illustrated on examples.
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"abstract": "Quantum duality principle is applied to study classical limits of quantum\nalgebras and groups. For a certain type of Hopf algebras the explicit procedure\nto construct both classical limits is presented. The canonical forms of\nquantized Lie-bialgebras are proved to be two-parametric varieties with two\nclassical limits called dual. When considered from the point of view of\nquantized symmetries such varieties can have boundaries that are noncommutative\nand noncocommutative. In this case the quantum duality and dual limits still\nexist while instead of Lie bialgebra one has a pair of tangent vector fields.\nThe properties of these constructions called quantizations of Hopf pairs are\nstudied and illustrated on examples.",
"arxiv_id": "q-alg/9506025",
"authors": [
"V. D. Lyakhovsky"
],
"categories": [
"q-alg",
"math.QA"
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"title": "Classical Limits, Quantum Duality and Lie-Poisson Structures",
"url": "https://arxiv.org/abs/q-alg/9506025"
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