Dual affine quantum groups
Identifieur interne : 000192 ( Istex/Curation ); précédent : 000191; suivant : 000193Dual affine quantum groups
Auteurs : Fabio GavariniSource :
- Mathematische Zeitschrift [ 0025-5874 ] ; 2000-05-01.
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Abstract
Abstract.: Let $\hat{\mathfrak{g}}$ be an untwisted affine Kac-Moody algebra, with its Sklyanin-Drinfel'd structure of Lie bialgebra, and let $\hat{\mathfrak{h}}$ be the dual Lie bialgebra. By dualizing the quantum double construction – via formal Hopf algebras – we construct a new quantum group $U_q (\hat\mathfrak{h}})$ , dual of $U_q (\hat\mathfrak{g}})$ . Studying its specializations at roots of 1 (in particular, its semi-classical limits), we prove that it yields quantizations of $\hat{\mathfrak{g}}$ and $\widehat{G}^\infty$ (the formal Poisson group attached to $\hat{\mathfrak{g}}$ ), and we construct new quantum Frobenius morphisms. The whole picture extends to the untwisted affine case the results known for quantum groups of finite type.
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DOI: 10.1007/s002090050502
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Fabio Gavarini<affiliation><mods:affiliation>Università degli Studi di Roma “Tor Vergata”, Dipartimento di Matematica, Via della Ricerca Scientifica 1, I-00133 Roma, Italy (e-mail: gavarini@mat.uniromA2.it), IT</mods:affiliation><wicri:noCountry code="subField">IT</wicri:noCountry></affiliation>Le document en format XML
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