Timeline for Does there exist any "quantum Lie algebra" embeded into the quantum enveloping algebra U_q(g)?
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| Apr 17, 2012 at 16:50 | comment | added | Nicola Ciccoli | @Alexander Thanks. I am not sure I caught the point of Morozov-Vinet's paper. But let me add here that the sudden switch form $u_h(\mathfrak g)$ to $U_q(\mathfrak g)$ in my answer is due to the fact that group-likes are elements of the form $K=q^H$ where $H$ is in the Cartan of the original Lie algebra, and therefore do require power series in the formal setting but can be considered as generators on the global one. | |
| Apr 17, 2012 at 12:54 | comment | added | Alexander Chervov | @Nicola Ciccoli nice answer. Concerning the group-like elements let me point the paper "Free-Field Representation of Group Element for Simple Quantum Group" Alexei Morozov, Luc Vinet arxiv.org/abs/hep-th/9409093, their claim is that in quantum case group-like elements live in in U_q(g)\otimes Fun_q(G), and the formula exp(g) is substituted by roughly speaking by exp_q(g*t). It seems to me that this paper is not so well-known. | |
| Apr 17, 2012 at 9:53 | history | edited | Nicola Ciccoli | CC BY-SA 3.0 |
added 287 characters in body
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| Apr 17, 2012 at 8:44 | history | answered | Nicola Ciccoli | CC BY-SA 3.0 |