Geodesic
TWO DESCRIPTIONS OF THE QUANTUM AFFINE ALGEBRA Uv() VIA HALL ALGEBRA APPROACH
Glasgow mathematical journal, Tome 54 (2012) no. 2, pp. 283-307

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DOI

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().
DOI : 10.1017/S0017089511000607
Mots-clés : Primary 16T20, 18E30, Secondary 17B37 
BURBAN, IGOR; SCHIFFMANN, OLIVIER. TWO DESCRIPTIONS OF THE QUANTUM AFFINE ALGEBRA Uv() VIA HALL ALGEBRA APPROACH. Glasgow mathematical journal, Tome 54 (2012) no. 2, pp. 283-307. doi: 10.1017/S0017089511000607
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     title = {TWO {DESCRIPTIONS} {OF} {THE} {QUANTUM} {AFFINE} {ALGEBRA} {Uv()} {VIA} {HALL} {ALGEBRA} {APPROACH}},
     journal = {Glasgow mathematical journal},
     pages = {283--307},
     year = {2012},
     volume = {54},
     number = {2},
     doi = {10.1017/S0017089511000607},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089511000607/}
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