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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
Affiliation:
Mathematisches Institut, Universität Bonn, Endenicher Allee 60, D-53115 Bonn, Germany e-mail: [email protected]
OLIVIER SCHIFFMANN
Affiliation:
Département de Mathématiques Université Paris Sud Bâtiment 425 91405 Orsay CedexFrance e-mail: [email protected]
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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().

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2011

References

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