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# The Diamond Lemma for (multiplicative) preprojective algebras

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.

COVID-19 information for PI Residents and Visitors

Collection/Series:
Event Type:
Seminar
Scientific Area(s):
Event Date:
Thursday, November 14, 2019 - 13:30 to 15:00
Location:
Sky Room
Room #:
394