TL;DR
This paper introduces higher gentle algebras, explores their singularity categories, and shows they are Iwanaga-Gorenstein, with connections to cluster-tilted algebras of higher Auslander algebras of type A.
Contribution
It defines higher gentle algebras and establishes their properties, including their singularity categories and Gorenstein condition, linking them to cluster-tilted algebras.
Findings
Higher gentle algebras are Iwanaga-Gorenstein.
Singularity categories of higher gentle algebras are determined.
Cluster-tilted algebras of higher Auslander algebras of type A are higher gentle under certain conditions.
Abstract
We introduce higher gentle algebras. Our definition allows us to determine the singularity categories and subsequently show that higher gentle algebras are Iwanaga-Gorenstein. Under extra assumptions, we show that cluster-tilted algebras (in the sense of Oppermann-Thomas) of higher Auslander algebras of type are higher gentle.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons