On the Cremmer-Gervais quantizations of SL(n)

Details On the Cremmer-Gervais quantizations of SL(n) On the Cremmer-Gervais quantizations of SL(n)

1995-06-22

arxiv.org/abs/q-alg/9506018v1

Mathematics

Quantum Algebra

14 pages, AMS-Latex

Scientific paper

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 $U_{\bar{R}}(\frak{gl}(n-1))$ 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.

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