Noncommutative projective curves and quantum loop algebras

By O. Schiffmann. 2002

87 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/24658b7e198b81ea220a19055d02951e6b792f2a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. I. Burban
2. Michel van den Bergh
3. L. Hille
4. O. Schiffmann
5. Osamu Iyama
6. Tatiana Gateva-Ivanova
7. Raf Bocklandt
8. B. Keller

In Geometry and Topology

1. O. Schiffmann
2. I. Burban
3. L. Hille
4. Michel van den Bergh
5. Osamu Iyama
6. Yukinobu Toda
7. T. Bridgeland
8. B. Keller

In Statistical and Nonlinear Physics

1. I. Burban
2. Michel van den Bergh
3. L. Hille
4. O. Schiffmann
5. Osamu Iyama
6. Xiao-Wu Chen
7. Damien Calaque

Citations in the corpus

• Handbook of Tilting Theory: Fourier-Mukai transforms (2004, result): “Then an analogous result holds for those curves (see also [48]).”
• On the Hall algebra of an elliptic curve, I (2005, background): “There is a natural action of SL(2, Z) on the circle S 1 = (R 2 \ {0})/R +⋆ . Using the identification S 1 = R/2Z, we can uniquely lift this action to an f”