Prof. Haicheng Zhang, Nanjing Normal University Abstract: In this talk, I will briefly review the development of Hall algebras, starting from Gabriel’s theorem in the representation theory of quivers. Explicitly, I will give the definitions of Hall algebras associated to exact categories or triangulated categories (satisfying some finiteness conditions), and definitions of Ringel--Hall Lie algebras in the sense of Peng--Xiao. If time permits, I will show the realization of the entire quantum group via Hall algebras of 2-cyclic complexes. |
