dorsal/arxiv
View SchemaThe algebra A_{\hbar,\eta}(\hat{g}) and Infinite Hopf family of algebras
| Authors | Bo-Yu Hou, Liu Zhao, Xiang-Mao Ding |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9703046 |
| URL | https://arxiv.org/abs/q-alg/9703046 |
| DOI | 10.1016/S0393-0440(97)00079-X |
Abstract
New deformed affine algebras A_{\hbar,\eta}(\hat{g}) are defined for any simply-laced classical Lie algebra g, which are generalizations of the algebra A_{\hbar,\eta}(\hat{sl_2}) recently proposed by Khoroshkin, Lebedev and Pakuliak (KLP). Unlike the work of KLP, we associate to the new algebras the structure of an infinite Hopf family of algebras in contrast to the one containing only finite number of algebras introduced by KLP. Bosonic representation for A_{\hbar,\eta}(\hat{g}) at level 1 is obtained, and it is shown that, by repeated application of Drinfeld-like comultiplications, a realization of A_{\hbar,\eta}(\hat{g}) at any positive integer level can be obtained. For the special case of g=sl_{r+1}, (r+1)-dimensional evaluation representation is given. The corresponding intertwining operators are defined and the intertwining relations are also derived explicitly.
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"abstract": "New deformed affine algebras A_{\\hbar,\\eta}(\\hat{g}) are defined for any\nsimply-laced classical Lie algebra g, which are generalizations of the algebra\nA_{\\hbar,\\eta}(\\hat{sl_2}) recently proposed by Khoroshkin, Lebedev and\nPakuliak (KLP). Unlike the work of KLP, we associate to the new algebras the\nstructure of an infinite Hopf family of algebras in contrast to the one\ncontaining only finite number of algebras introduced by KLP. Bosonic\nrepresentation for A_{\\hbar,\\eta}(\\hat{g}) at level 1 is obtained, and it is\nshown that, by repeated application of Drinfeld-like comultiplications, a\nrealization of A_{\\hbar,\\eta}(\\hat{g}) at any positive integer level can be\nobtained. For the special case of g=sl_{r+1}, (r+1)-dimensional evaluation\nrepresentation is given. The corresponding intertwining operators are defined\nand the intertwining relations are also derived explicitly.",
"arxiv_id": "q-alg/9703046",
"authors": [
"Bo-Yu Hou",
"Liu Zhao",
"Xiang-Mao Ding"
],
"categories": [
"q-alg",
"math.QA"
],
"doi": "10.1016/S0393-0440(97)00079-X",
"title": "The algebra A_{\\hbar,\\eta}(\\hat{g}) and Infinite Hopf family of algebras",
"url": "https://arxiv.org/abs/q-alg/9703046"
},
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