Noncommutative projective curves and quantum loop algebras
Quantum Algebra
2007-05-23 v3 Rings and Algebras
Abstract
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.
Cite
@article{arxiv.math/0205267,
title = {Noncommutative projective curves and quantum loop algebras},
author = {Olivier Schiffmann},
journal= {arXiv preprint arXiv:math/0205267},
year = {2007}
}
Comments
Latex, 40 pages, 2 figures, analog of Kac's conjecture added; final version to appear