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Jul 22, 2014 at 18:35 answer added Steve Sawin timeline score: 5
Apr 9, 2013 at 16:41 answer added Nicola Ciccoli timeline score: 15
Apr 8, 2013 at 15:32 comment added Jan Grabowski This isn't a precise technical answer but the root of unity or not divide is (in ways that can be made precise) analogous to the characteristic zero versus characteristic p divide. Away from the root of unity case, most things are nice; in the root of unity case they go just as badly wrong as Lie algebras in characteristic p. (NB. The interesting shift here is that the characteristic of the actual field underlying $U_{q}(\mathfrak{g})$ isn't in the foreground: the split in behaviour described above happens even for $U_{q}(\mathfrak{g})$ as an algebra over the complex numbers.)
Apr 8, 2013 at 12:42 history asked Milen Stamatov CC BY-SA 3.0