Two descriptions of the quantum affine algebra Uv(sl̂ 2) via hall algebra approach

Abstract

We compare the reduced Drinfeld doubles of the composition subalgebras of the category of representations of the Kronecker quiver Q→ and the category of coherent sheaves on ℙ1. Using this approach, we show that the Drinfeld-Beck isomorphism for the quantized enveloping algebra Uv(sl̂2) is a corollary of an equivalence between the derived categories Db(Rep(Q→)) and D b(Coh(ℙ1)). This technique allows to reprove several results on the integral form of Uv(sl̂2). © 2012 Glasgow Mathematical Journal Trust.