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TWO DESCRIPTIONS OF THE QUANTUM AFFINE ALGEBRA Uv() VIA HALL ALGEBRA APPROACH

Published online by Cambridge University Press:  12 December 2011

IGOR BURBAN  and
OLIVIER SCHIFFMANN
IGOR BURBAN
Affiliation:
Mathematisches Institut, Universität Bonn, Endenicher Allee 60, D-53115 Bonn, Germany e-mail: burban@math.uni-bonn.de
OLIVIER SCHIFFMANN
Affiliation:
Département de Mathématiques Université Paris Sud Bâtiment 425 91405 Orsay CedexFrance e-mail: Olivier.Schiffmann@math.u-psud.fr
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Abstract

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We compare the reduced Drinfeld doubles of the composition subalgebras of the category of representations of the Kronecker quiver and the category of coherent sheaves on ℙ1. Using this approach, we show that the Drinfeld–Beck isomorphism for the quantized enveloping algebra Uv() is a corollary of an equivalence between the derived categories Db(Rep()) and Db(Coh(ℙ1)). This technique allows to reprove several results on the integral form of Uv().

Keywords

Primary 16T2018E30Secondary 17B37
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 54 , Issue 2 , May 2012 , pp. 283 - 307
Copyright
Copyright © Glasgow Mathematical Journal Trust 2011

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