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TWO DESCRIPTIONS OF THE QUANTUM AFFINE ALGEBRA Uv() VIA HALL ALGEBRA APPROACH
IGOR BURBAN, OLIVIER SCHIFFMANN
Journal:

Glasgow Mathematical Journal / Volume 54 / Issue 2 / May 2012

Published online by Cambridge University Press:

12 December 2011, pp. 283-307

Print publication:

May 2012
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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().