ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sun, 11 Jul 2021 18:20:13 +0200Obtaining admissible relations for acyclic tree quivers with Sage for QPAhttps://ask.sagemath.org/question/57962/obtaining-admissible-relations-for-acyclic-tree-quivers-with-sage-for-qpa/Let $Q$ be a finite acyclic quiver which is a tree as an undirected graph.
>Question: Is there a way to use Sage to obtain all admissible ideals $I$ in the quiver algebra $KQ$ (those are simply the ideals generated by paths of lenghts at least two)?
The output should be so that it can be read by the GAP-package QPA.
Here an example:
The input is the quiver $Q$ given by
Quiver( ["v1","v2","v3","v4"], [["v1","v2","a1"],["v2","v3","a2"],["v3","v4","a3"]] )
The output is the 5 admissible ideals given as follows:
[ [],[ a1*a2, a2*a3 ], [ a2*a3 ], [ a1*a2 ], [ a1*a2*a3 ] ]
(more generally the number of admissible ideals for a linear oriented line quiver is given by the Catalan numbers)Sun, 11 Jul 2021 18:20:13 +0200https://ask.sagemath.org/question/57962/obtaining-admissible-relations-for-acyclic-tree-quivers-with-sage-for-qpa/