摘要: We show that the Hall algebra of category coherent sheaves on a weighted projective line over finite field provides a realization (quantized) enveloping certain nilpotent subalgebra affinization corresponding Kac-Moody algebra. In particular, this yields geometric realization quantized elliptic (or $2$-toroidal) algebras types $D_4^{(1,1)}$, $E^{(1,1)}_6$, $E^{(1,1)}_7$, and $E_{8}^{(1,1)}$ in terms sheaves on weighted lines genus one or, equivalently, terms of equivariant on curves.
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