Calabi–Yau properties of Postnikov diagrams

Pressland, M. (2022) Calabi–Yau properties of Postnikov diagrams. Forum of Mathematics, Sigma, 10, e56. (doi: 10.1017/fms.2022.52)

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 [43]. 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 [18]. We show that our categorification can be realised as a full extension closed subcategory of Jensen–King–Su’s Grassmannian cluster category [28], in a way compatible with their bijection between rank 1 modules and Plücker coordinates.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Pressland, Dr Matthew
• Authors: Pressland, M.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Forum of Mathematics, Sigma
• Publisher: Cambridge University Press
• ISSN: 2050-5094
• ISSN (Online): 2050-5094
• Published Online: 21 July 2022
• Copyright Holders: Copyright © 2022 The Authors
• First Published: First published in Forum of Mathematics, Sigma 10:e56
• Publisher Policy: Reproduced under a Creative Commons licence