The Small Quantum Group as a Quantum Double
Author(s)Etingof, Pavel I.; Gelaki, Shlomo
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We prove that the quantum double of the quasi-Hopf algebra View the MathML source of We prove that the quantum double of the quasi-Hopf algebra Aq(g) of dimension ndimg attached in [P. Etingof, S. Gelaki, On radically graded finite-dimensional quasi-Hopf algebras, Mosc. Math. J. 5 (2) (2005) 371–378] 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 deequivariantization of tensor categories.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Journal of Algebra
Etingof, Pavel, and Shlomo Gelaki. “The Small Quantum Group as a Quantum Double.” Journal of Algebra 322.7 (2009) : 2580-2585.
Author's final manuscript