The Small Quantum Group as a Quantum Double

The Small Quantum Group as a Quantum Double

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...

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Bibliographic Details
Main Authors: Etingof, Pavel I. (Contributor), Gelaki, Shlomo (Author)
Other Authors: Massachusetts Institute of Technology. Department of Mathematics (Contributor)
Format: Article
Language:English
Published: Elsevier, 2011-06-09T12:38:10Z.
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Summary: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.
National Science Foundation (U.S.) (Grant No. DMS-0504847)
Israel Science Foundation (grant No. 125/05)
BSF (grant No. 2002040)

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