PIRSA:19110080

The Diamond Lemma for (multiplicative) preprojective algebras

(2019). The Diamond Lemma for (multiplicative) preprojective algebras. Perimeter Institute. https://pirsa.org/19110080

The Diamond Lemma for (multiplicative) preprojective algebras. Perimeter Institute, Nov. 14, 2019, https://pirsa.org/19110080 

          @misc{ pirsa_PIRSA:19110080,
            doi = {10.48660/19110080},
            url = {https://pirsa.org/19110080},
            author = {},
            keywords = {Mathematical physics},
            language = {en},
            title = {The Diamond Lemma for (multiplicative) preprojective algebras},
            publisher = {Perimeter Institute},
            year = {2019},
            month = {nov},
            note = {PIRSA:19110080 see, \url{https://pirsa.org}}
          }
Talk number
PIRSA:19110080
Collection
Talk Type
Subject
Abstract

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.