Tom Bridgeland : Hall algebras and quantum groups

Posted by Mihnea Popa , part of the Departmental Colloquium.

At

March 22, 2013, 3 p.m.

In

Lecture Center C4 (please note special location)

Abstract

A celebrated theorem of Ringel gives a neat formula-free description of positive parts of quantized enveloping algebras in terms of categories of quiver representations. The crucial ingredient is the notion of the Hall algebra of an abelian category. I will explain this construction, give a precise statement of Ringel's result, and then describe a generalization which gives a similar formula-free description for the full quantum group.