Representation theoretic and geometric approach to constructing quantum groups

Time: July 6 (Friday) 15:00-16:00

Place: N902

Speaker: Zhongzhu Lin (Kansas State University)

Title: Representation theoretic and geometric approach to constructing quantum groups.

Abstract: Since Gabriel's discovery of the one-to-one correspondence between indecomposable representations of a Dynkin quiver and the positive roots of the simple Lie algebra corresponding to the Dynkin diagram,  quiver representation theory has been closely tied to Lie algebras in many ways. Ringel's reconstruction of quantum enveloping algebras in terms of Hall algebras of the representations of the Dynkin quiver over finite has lifted connection to a new level and inspired Lusztig to construct the canonical basis. In this talk, I will outline both approaches to constructing quantum groups as well as other subsequent approaches such as Bridgeland's approach in terms of two steps complexes and two parameter quantum groups arising from geometric approach by Fan and Li. 

Zhongzhu Lin gives a talk on quantum group constructions.