Pressland, M orcid.org/0000-0002-9631-3583 (2020) Mutation of frozen Jacobian algebras. Journal of Algebra, 546. pp. 236-273. ISSN 0021-8693
Abstract
We survey results on mutations of Jacobian algebras, while simultaneously extending them to the more general setup of frozen Jacobian algebras, which arise naturally from dimer models with boundary and in the context of the additive categorification of cluster algebras with frozen variables via Frobenius categories. As an application, we show that the mutation of cluster-tilting objects in various such categorifications, such as the Grassmannian cluster categories of Jensen–King–Su, is compatible with Fomin–Zelevinsky mutation of quivers. We also describe an extension of this combinatorial mutation rule allowing for arrows between frozen vertices, which the quivers arising from categorifications and dimer models typically have.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © 2019 Elsevier Inc. All rights reserved. This is an author produced version of an article published in Journal of Algebra. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Quiver with potential; Jacobian algebra; Mutation; Frobenius category; Dimer model |
Dates: |
|
Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 03 Apr 2020 14:41 |
Last Modified: | 14 Nov 2021 01:38 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.jalgebra.2019.10.035 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:159074 |
Commentary/Response Threads
- Pressland, M Mutation of frozen Jacobian algebras. (deposited 03 Apr 2020 14:41) [Currently Displayed]
Download
Filename: Mutation of frozen Jacobian algebras - revised.pdf
Licence: CC-BY-NC-ND 4.0