10.48660/19110080
Perimeter Institute
Perimeter Institute
The Diamond Lemma for (multiplicative) preprojective algebras
Perimeter Institute
2019
Video Recording
Mathematical physics
2019-11-14T18:30:00
English
https://pirsa.org/19110080
video/mp4
<p>Bergman's Diamond Lemma for ring theory gives an algorithm to produce a (non-canonical) basis for a ring presented by generators and relations. After demonstrating this algorithm in concrete, geometrically-minded examples, I'll turn to preprojective algebras and their multiplicative counterparts. Using the Diamond Lemma, I'll reprove a few classical results for preprojective algebras. Then I'll propose a conjectural basis for multiplicative preprojective algebras. Finally I'll explain why the set is a basis in the case of multiplicative preprojective algebras for quivers containing a cycle, the subject of joint work with Travis Schedler.</p>