Maximum antichains in posets of quiver representations

Gellert F, Lampe P (2018)
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 59(1): 1-20.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
Abstract / Bemerkung
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.
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Zeitschriftentitel
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
Band
59
Zeitschriftennummer
1
Seite
1-20
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Gellert F, Lampe P. Maximum antichains in posets of quiver representations. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry. 2018;59(1):1-20.
Gellert, F., & Lampe, P. (2018). Maximum antichains in posets of quiver representations. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 59(1), 1-20. doi:10.1007/s13366-017-0359-1
Gellert, F., and Lampe, P. (2018). Maximum antichains in posets of quiver representations. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 59, 1-20.
Gellert, F., & Lampe, P., 2018. Maximum antichains in posets of quiver representations. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 59(1), p 1-20.
F. Gellert and P. Lampe, “Maximum antichains in posets of quiver representations”, Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, vol. 59, 2018, pp. 1-20.
Gellert, F., Lampe, P.: Maximum antichains in posets of quiver representations. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry. 59, 1-20 (2018).
Gellert, Florian, and Lampe, Philipp. “Maximum antichains in posets of quiver representations”. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 59.1 (2018): 1-20.
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arXiv: 1608.03446

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