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arXiv · 0902.0332

The small quantum group as a quantum double

Pavel Etingof·Shlomo Gelaki
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Abstract

We prove that the quantum double of the quasi-Hopf algebra A_q(g) of dimension n^{dim g} attached in arXiv:math/0403096 to a simple complex Lie algebra g and a primitive root of unity q of order n^2 is equivalent to Lusztig's small quantum group u_q(g) (under some conditions on n). We also give a conceptual construction of A_q(g) using the notion of de-equivariantization of tensor categories.

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Pavel Etingof, Shlomo Gelaki. 2009-05-27. The small quantum group as a quantum double. https://arxiv.org/abs/0902.0332

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