Maximum antichains in posets of quiver representations

Gellert, Florian; Lampe, Philipp

Abstract

We study maximum antichains in two posets related to quiver representations. Firstly, we consider the set of isomorphism classes of indecomposable representations ordered by inclusion. For various orientations of the Dynkin diagram of type A we construct a maximum antichain in the poset. Secondly, we consider the set of subrepresentations of a given quiver representation, again ordered by inclusion. It is a finite set if we restrict to linear representations over finite fields or to representations with values in the category of pointed sets. For particular situations we prove that this poset is Sperner.

Citation

Gellert, F., & Lampe, P. (2018). Maximum antichains in posets of quiver representations. Contributions to Algebra and Geometry, 59(1), 1-20. https://doi.org/10.1007/s13366-017-0359-1

• Journal Article Type: Article
• Acceptance Date: Sep 12, 2017
• Online Publication Date: Oct 6, 2017
• Publication Date: Mar 1, 2018
• Deposit Date: Oct 10, 2017
• Publicly Available Date: Oct 10, 2017
• Journal: Contributions to Algebra and Geometry
• Print ISSN: 0138-4821
• Electronic ISSN: 2191-0383
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 59
• Issue: 1
• Pages: 1-20
• DOI: https://doi.org/10.1007/s13366-017-0359-1
• Public URL: https://durham-repository.worktribe.com/output/1346866