The category of coherent sheaves over a weighted projective line and loop algebras

Abstract

In this survey paper, we introduce the approach to construct complex Lie algebras via root categories. For the category of coherent sheaves over a weighted projective line,the approach provides a realization of the loop algebra of the Kac-Moody algebra associated with the corresponding star graph.As an application, we categorify the Weyl group of the corresponding Kac-Moody algebra.