Semi-invariants for gentle algebras
Andrew T. Carroll, Jerzy Weyman · Contemporary mathematics - American Mathematical Society · 2013
In this article we give an algorithm for determining the generators and relations for the rings of semi-invariant functions on irreducible components of R e p A ( β ) \mathrm {Rep}_A(\beta ) when A A is a (acyclic) gentle algebra and β \beta is a dimension vector. 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 as 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.