Mutation of frozen Jacobian algebras

Pressland, M. (2020) Mutation of frozen Jacobian algebras. Journal of Algebra, 546, pp. 236-273. (doi: 10.1016/j.jalgebra.2019.10.035)

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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.

Item Type:Articles
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:Journal of Algebra
ISSN (Online):1090-266X
Published Online:14 November 2019

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