On the Cremmer-Gervais quantizations of SL(n)

Abstract

Non-standard quantum groups $C_R[GL(n)]$ and $C_R[SL(n)]$ are constructed for a two parameter version of the Cremmer-Gervais $R$-matrix. An epimorphism is constructed from $C_R[GL(n)]$ onto the restricted dual $U_{\bar{R}}(\mathfrak{gl}(n-1))$ associated to a related smaller $R$-matrix of the same form. A related result is proved concerning factorizable Lie bialgebras. For any such Lie bialgebra, the dual Lie bialgebra has a canonical homomorphic image which is again factorizable.

14 pages, AMS-Latex

References in corpus (2)

• Algebraic structure of multi-parameter quantum groups
• Poincaré series of quantum matrix bialgebras determined by a pair of quantum spaces

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• Quantization of certain skew-symmetric solutions of the classical Yang-Baxter equation
• The Cremmer-Gervais solution of the Yang-Baxter equation
• Double quantum groups and Iwasawa decomposition