Minimal generating set for semi-invariants of quivers of dimension two
A.A. Lopatin
TL;DR
This paper establishes a minimal generating set for the algebra of semi-invariants of quivers of dimension two, using determinants and traces, and describes relations among them.
Contribution
It provides the first explicit minimal generating set for semi-invariants of quivers of dimension two over any field, including relations among generators.
Findings
Generated semi-invariants by determinants and traces.
Described relations modulo decomposable semi-invariants.
Applicable over fields of arbitrary characteristic.
Abstract
A minimal (by inclusion) generating set for the algebra of semi-invariants of a quiver of dimension (2,...,2) is established over an infinite field of arbitrary characteristic. The mentioned generating set consists of the determinants of generic matrices and the traces of tree paths of pairwise different multidegrees, where in the case of characteristic different from two we take only admissible paths. As a consequence, we describe relations modulo decomposable semi-invariants.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Combinatorial Mathematics · Molecular spectroscopy and chirality