2010/02/05 by Rujing Dou, Yong Jiang, Dou, Rujing +3
Mathematics · Physics and Astronomy · #14H60 #17B37 #18F20 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1002.1316
openalex publication_date 2010/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The quantum loop algebra Uv(L\mathfrakg) was defined as a generalization of the Drinfeld's new realization of the quantum affine algebra to the loop algebra of any Kac-Moody algebra \mathfrakg. It has been shown by Schiffmann that the Hall algebra of the category of coherent sheaves on a weighted projective line is closely related to the quantum loop algebra Uv(L\mathfrakg), for some \mathfrakg with a star-shaped Dynkin diagram. In this paper we study Drinfeld's presentation of Uv(L\mathfrakg) in the double Hall algebra setting, based on Schiffmann's work. We explicitly find out a collection of generators of the double composition algebra DC(\Coh(\mathbbX)) and verify that they satisfy all the Drinfeld relations.