An algorithm for the periodicity of deformed preprojective algebras of Dynkin types E6, E7 and E8

作者：

Highlights：

• We construct a numeric algorithm for completing the proof of a conjecture asserting that all deformed preprojective algebras of generalized Dynkin type are periodic.

• We obtain an algorithmic procedure showing that non-trivial deformed preprojective algebras of Dynkin types E7 and E8 exist only in characteristic 2.

• We show that deformed preprojective algebras of Dynkin types E6, E7 and E8 are periodic.

摘要

•We construct a numeric algorithm for completing the proof of a conjecture asserting that all deformed preprojective algebras of generalized Dynkin type are periodic.•We obtain an algorithmic procedure showing that non-trivial deformed preprojective algebras of Dynkin types E7 and E8 exist only in characteristic 2.•We show that deformed preprojective algebras of Dynkin types E6, E7 and E8 are periodic.

论文关键词：Preprojective algebra,Deformed preprojective algebra,Self-injective algebra,Periodic algebra,System of equations

论文评审过程：Received 7 June 2020, Revised 2 April 2021, Accepted 6 April 2021, Available online 17 June 2021, Version of Record 17 June 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126289