The small quantum group as a quantum double
Abstract
We prove that the quantum double of the quasi-Hopf algebra Aq(g) of dimension ndim g attached in arXiv:math/0403096 to a simple complex Lie algebra g and a primitive root of unity q of order n2 is equivalent to Lusztig's small quantum group uq(g) (under some conditions on n). We also give a conceptual construction of Aq(g) using the notion of de-equivariantization of tensor categories.
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