The Small Quantum Group as a Quantum Double
Name
Etingof J Algebbra 2009.pdf
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145.39 KB
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Author(s)
Etingof, Pavel I.
Gelaki, Shlomo
Date Issued
July 2009
Journal
Journal of Algebra
Publisher
Elsevier
Citation
Etingof, Pavel, and Shlomo Gelaki. “The Small Quantum Group as a Quantum Double.” Journal of Algebra 322.7 (2009) : 2580-2585.
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1016/j.jalgebra.2009.05.046
