Noncommutative projective curves and quantum loop algebras

Details Noncommutative projective curves and quantum loop algebras Noncommutative projective curves and quantum loop algebras

2002-05-25

arxiv.org/abs/math/0205267v3

Mathematics

Quantum Algebra

Latex, 40 pages, 2 figures, analog of Kac's conjecture added; final version to appear

Scientific paper

We generalize a theorem of Kapranov by showing that the Hall algebra of the category of coherent sheaves on a weighted projective line (over a finite field) provides a realization of the (quantized) enveloping algebra of a certain nilpotent subalgebra of the affinization of the correponding Kac-Moody algebra. In particular this yieds a geometric realization of the quantized enveloping algebra of 2-toroidal (or elliptic) algebras of types D_4, E_6, E_7 or E_8 in terms of weighted projective lines of genus one.

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