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• W2892316250 abstract "Over a finite-dimensonal algbera $A$, simple $A$-modules that have projective dimension one have special properties. For example, Geigle-Lenzing studied them in connection to homological epimorphisms of rings, and they have also appeared in work concerning the finitistic dimension conjecture. If we however work in a $d$-cluster-tilting subcategory, then not all simples are contained in this subcategory. In this context, a replacement might be to work with idempotent ideals instead, and utilise the theory of Auslander-Platzeck-Todorov. We introduce the notion of a fabric idempotent as an analogue of the localising modules studied by Chen-Krause, and to illustrate the theory we show that they provide rich combinatorial properties. An application is to extend the classification of singularity categories of Nakayama algebras by Chen-Ye to higher Nakayama algebras." @default.
• W2892316250 created "2018-09-27" @default.
• W2892316250 creator A5072329985 @default.
• W2892316250 date "2018-03-19" @default.
• W2892316250 modified "2023-09-27" @default.
• W2892316250 title "Fabric idempotents and homological dimensions" @default.
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