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.
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 language | English |
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Pages (from-to) | 185-212 |
Journal | Proceedings of the London Mathematical Society |
Volume | 113 |
Issue number | 2 |
Early online date | 13 Jul 2016 |
DOIs | |
Publication status | Published - 2 Aug 2016 |