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Homological conditions on locally gentle algebras

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arxiv 2409.08333 v2 pith:WVGPYURD submitted 2024-09-12 math.RT

S. Ford , A. Oswald , J.J. Zhang This is my paper · ORCID
classification math.RT
keywords algebrasgentlelocallyalgebraartin-schelterhomologicalanaloguebeen
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Gentle algebras are a class of special biserial algebra whose representation theory has been thoroughly described. In this paper, we consider the infinite dimensional generalizations of gentle algebras, referred to as locally gentle algebras. We give combinatorial descriptions of the center, prime spectrum, and homological dimensions of a locally gentle algebra, including an explicit injective resolution. We classify when these algebras are Artin-Schelter Gorenstein, Artin-Schelter regular, and Cohen-Macaulay, and provide an analogue of Stanley's theorem for locally gentle algebras.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Cluster algebraic interpretation of generalized Markov numbers and their matrixizations

    math.CO 2025-07 conditional novelty 7.0 of 10

    Two new families of cluster Cohn and Markov-monodromy matrices for generalized Markov cluster algebras are introduced, fully classified, and made explicit via weighted fence posets whose order ideals expand cluster variables.

  2. Global dimension of a string algebra

    math.RT 2026-07 conditional novelty 6.0 of 10

    The global dimension of a string algebra equals the maximum length of minimal relation chains beginning with an arrow, and is infinite precisely when an infinite such chain exists.

  3. Homological Bounds of Gentle algebras

    math.RT 2025-08 conditional novelty 6.0 of 10

    Under a strong-source or strong-sink condition on maximal forbidden paths, gentle algebras satisfy hb.dim A ≤ 2·gl.dim A − 1 (or 2·f.dim A − 1), yielding a new quasi-tilted criterion when gl.dim A = 2.

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