Exceptional modules over wild canonical algebras
Volume 162 / 2020
Colloquium Mathematicum 162 (2020), 159-180
MSC: 16G20, 14F05, 16G60.
DOI: 10.4064/cm7876-8-2019
Published online: 15 April 2020
Abstract
We show that in a certain sense “almost all” exceptional modules over wild canonical algebra $\Lambda (\underline p ,\underline\lambda )$ can be described by matrices with entries of the form $\lambda _i-\lambda _j$, where $\lambda _i, \lambda _j$ are elements from the parameter sequence $\underline\lambda $.
The proof is based on Schofield induction for sheaves in the associated categories of weighted projective lines (Kędzierski and Meltzer 2013) and an extended version of Ringel’s proof of the $0, 1$ matrix property of exceptional representations for finite acyclic quivers.
