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arXiv · 1912.12475

Calabi-Yau properties of Postnikov diagrams

Matthew Pressland
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Abstract

We show that the dimer algebra of a connected Postnikov diagram in the disc is bimodule internally 3-Calabi-Yau in the sense of the author's earlier work. As a consequence, we obtain an additive categorification of the cluster algebra associated to the diagram, which (after inverting frozen variables) is isomorphic to the homogeneous coordinate ring of a positroid variety in the Grassmannian by a recent result of Galashin and Lam. We show that our categorification can be realised as a full extension closed subcategory of Jensen-King-Su's Grassmannian cluster category, in a way compatible with their bijection between rank 1 modules and Pl\"ucker coordinates.

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BibTeXRIS

Matthew Pressland. 2019-12-28. Calabi-Yau properties of Postnikov diagrams. https://doi.org/10.1017/fms.2022.52

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