dorsal/arxiv
View SchemaYangian Algebras and Classical Riemann Problems
| Authors | S. Khoroshkin, D. Lebedev, S. Pakuliak |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9712057 |
| URL | https://arxiv.org/abs/q-alg/9712057 |
Abstract
We investigate different Hopf algebras associated to Yang's solution of quantum Yang-Baxter equation. It is shown that for the precise definition of the algebra one needs the commutation relations for the deformed algebra of formal currents and the specialization of the Riemann problem for the currents. Two different Riemann problems are considered. They lead to the central extended Yangian double associated with ${sl}_2$ and to the degeneration of scaling limit of elliptic affine algebra. Unless the defining relations for the generating functions of the both algebras coincide their properties and the theory of infinite-dimensional representations are quite different. We discuss also the Riemann problem for twisted algebras and for scaled elliptic algebra.
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"abstract": "We investigate different Hopf algebras associated to Yang\u0027s solution of\nquantum Yang-Baxter equation. It is shown that for the precise definition of\nthe algebra one needs the commutation relations for the deformed algebra of\nformal currents and the specialization of the Riemann problem for the currents.\nTwo different Riemann problems are considered. They lead to the central\nextended Yangian double associated with ${sl}_2$ and to the degeneration of\nscaling limit of elliptic affine algebra. Unless the defining relations for the\ngenerating functions of the both algebras coincide their properties and the\ntheory of infinite-dimensional representations are quite different. We discuss\nalso the Riemann problem for twisted algebras and for scaled elliptic algebra.",
"arxiv_id": "q-alg/9712057",
"authors": [
"S. Khoroshkin",
"D. Lebedev",
"S. Pakuliak"
],
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"q-alg",
"math.QA"
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"title": "Yangian Algebras and Classical Riemann Problems",
"url": "https://arxiv.org/abs/q-alg/9712057"
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