dorsal/arxiv
View SchemaElliptic quantum groups $E_{\tau,\eta}(sl_2)$ and quasi-Hopf algebras
| Authors | B. Enriquez, G. Felder |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9703018 |
| URL | https://arxiv.org/abs/q-alg/9703018 |
| DOI | 10.1007/s002200050407 |
Abstract
We construct an algebra morphism from the elliptic quantum group $E_{\tau,\eta}(sl_2)$ to a certain elliptic version of the ``quantum groups in higher genus'' studied by V. Rubtsov and the first author. This provides an embedding of $E_{\tau,\eta}(sl_2)$ in an algebra ``with central extension''. In particular we construct $L^{\pm}$-operators obeying a dynamical version of the Reshetikhin--Semenov-Tian-Shansky relations. To do that, we construct the factorization of a certain twist of the latter algebra, that automatically satisfies the ``twisted cocycle condition'' of O. Babelon, D. Bernard and E. Billey, and therefore provides a solution of the dynamical Yang-Baxter equation.
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"abstract": "We construct an algebra morphism from the elliptic quantum group\n$E_{\\tau,\\eta}(sl_2)$ to a certain elliptic version of the ``quantum groups in\nhigher genus\u0027\u0027 studied by V. Rubtsov and the first author. This provides an\nembedding of $E_{\\tau,\\eta}(sl_2)$ in an algebra ``with central extension\u0027\u0027. In\nparticular we construct $L^{\\pm}$-operators obeying a dynamical version of the\nReshetikhin--Semenov-Tian-Shansky relations. To do that, we construct the\nfactorization of a certain twist of the latter algebra, that automatically\nsatisfies the ``twisted cocycle condition\u0027\u0027 of O. Babelon, D. Bernard and E.\nBilley, and therefore provides a solution of the dynamical Yang-Baxter\nequation.",
"arxiv_id": "q-alg/9703018",
"authors": [
"B. Enriquez",
"G. Felder"
],
"categories": [
"q-alg",
"math.QA"
],
"doi": "10.1007/s002200050407",
"title": "Elliptic quantum groups $E_{\\tau,\\eta}(sl_2)$ and quasi-Hopf algebras",
"url": "https://arxiv.org/abs/q-alg/9703018"
},
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