Maximum antichains in posets of quiver representations

Gellert, Florian and Lampe, P. (2018) Maximum antichains in posets of quiver representations. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 59 (1). pp. 1-20. ISSN 0138-4821. (doi:https://doi.org/10.1007/s13366-017-0359-1) (Full text available)

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Official URL
https://doi.org/10.1007/s13366-017-0359-1

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.

Item Type: Article
Uncontrolled keywords: Quiver representations, Subrepresentations, Posets, Maximum antichains
Subjects: Q Science > QA Mathematics (inc Computing science) > QA165 Combinatorics
Q Science > QA Mathematics (inc Computing science) > QA171 Representation theory
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Philipp Lampe
Date Deposited: 16 Jul 2018 16:53 UTC
Last Modified: 19 Jul 2018 15:13 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/67642 (The current URI for this page, for reference purposes)
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