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On self-orthogonal modules in Iwanaga-Gorenstein rings

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arxiv 2303.10433 v1 pith:G7UIKXRA submitted 2023-03-18 math.RT math.RA

Rene Marczinzik This is my paper · ORCID
classification math.RTmath.RA
keywords conjectureenomotoiwanaga-gorensteinmoduleringsself-orthogonalalgebrasanswers
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abstract

Let $A$ be an Iwanaga-Gorenstein ring. Enomoto conjectured that a self-orthogonal $A$-module has finite projective dimension. We prove this conjecture for $A$ having the property that every indecomposable non-projective maximal Cohen-Macaulay module is periodic. This answers a question of Enomoto and shows the conjecture for monomial quiver algebras and hypersurface rings.

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Cited by 1 Pith paper

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  1. Tilting-completion for gentle algebras

    math.RT 2024-12 conditional novelty 6.0 of 10

    For gentle algebras, almost-tilting modules always complete to tilting modules with at most 2n complements, matching a modified version of Happel's conjecture.

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