The small quantum group as a quantum double
Quantum Algebra
2009-05-27 v3
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.
Keywords
Cite
@article{arxiv.0902.0332,
title = {The small quantum group as a quantum double},
author = {Pavel Etingof and Shlomo Gelaki},
journal= {arXiv preprint arXiv:0902.0332},
year = {2009}
}
Comments
latex, 6 pages; proof of Theorem 4.1 added, a few references added