Semi-Invariants for Gentle String Algebras
Representation Theory
2011-06-07 v1
Abstract
In this article we give an algorithm for determining the generators and relations for the rings of semi-invariant functions on irreducible components of representation spaces for gentle string algebras. These rings of semi-invariants turn out to be semigroup rings to which we can associate a so-called matching graph. Under this association, generators for the semigroup can be seen by certain walks on this graph, and relations are given by certain configurations in the graph. This allows us to determine degree bounds for the generators and relations of these rings. We furthermore show that these bounds also hold for acyclic string algebras in general.
Cite
@article{arxiv.1106.0774,
title = {Semi-Invariants for Gentle String Algebras},
author = {Andrew T. Carroll and Jerzy Weyman},
journal= {arXiv preprint arXiv:1106.0774},
year = {2011}
}
Comments
42 pages