A categorification of Grassmannian cluster algebras

Bernt Tore Jensen, Alastair D. King, Xiuping Su

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

We describe a ring whose category of Cohen-Macaulay modules
provides an additive categorication the cluster algebra structure on the homogeneous coordinate ring of the Grassmannian of k-planes in n-space. More
precisely, there is a cluster character dened on the category which maps the
rigid indecomposable objects to the cluster variables and the maximal rigid objects
to clusters. This is proved by showing that the quotient of this category by
a single projective-injective object is Geiss-Leclerc-Schroer's category Sub Qk,
which categories the coordinate ring of the big cell in this Grassmannian.
Original languageEnglish
Pages (from-to)185-212
JournalProceedings of the London Mathematical Society
Volume113
Issue number2
Early online date13 Jul 2016
DOIs
Publication statusPublished - 2 Aug 2016

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Categorification
Cluster Algebra
Grassmannian
Ring
Cohen-Macaulay Module
Homogeneous coordinates
Injective
Quotient
Cell
Object

Cite this

A categorification of Grassmannian cluster algebras. / Jensen, Bernt Tore; King, Alastair D.; Su, Xiuping.

In: Proceedings of the London Mathematical Society, Vol. 113, No. 2, 02.08.2016, p. 185-212.

Research output: Contribution to journalArticle

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