Noncommutative projective curves and quantum loop algebras
Schiffmann, Olivier
Duke Math. J., Tome 121 (2004) no. 1, p. 113-168 / Harvested from Project Euclid
We show 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 corresponding Kac-Moody algebra. In particular, this yields a geometric realization of the quantized enveloping algebra of elliptic (or $2$-toroidal) algebras of types $D_4^{(1,1)}$, $E^{(1,1)}_6$, $E^{(1,1)}_7$, and $E_{8}^{(1,1)}$ in terms of coherent sheaves on weighted projective lines of genus one or, equivalently, in terms of equivariant coherent sheaves on elliptic curves.
Publié le : 2004-01-15
Classification:  22E,  16G,  18F
@article{1072058751,
     author = {Schiffmann, Olivier},
     title = {Noncommutative projective curves and quantum loop algebras},
     journal = {Duke Math. J.},
     volume = {121},
     number = {1},
     year = {2004},
     pages = { 113-168},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1072058751}
}
Schiffmann, Olivier. Noncommutative projective curves and quantum loop algebras. Duke Math. J., Tome 121 (2004) no. 1, pp.  113-168. http://gdmltest.u-ga.fr/item/1072058751/