Auslander-Reiten triangles in subcategories

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dc.creatorJorgensen, Peter
dc.date2006-06-26
dc.date.accessioned2026-07-07T07:17:42Z
dc.date.available2026-07-07T07:17:42Z
dc.descriptionThis paper introduces Auslander-Reiten triangles in subcategories of triangulated categories. The main theorem of the paper shows that there is a close connection with covers and envelopes, also known as minimal right- and left-approximations. Namely, under suitable assumptions, if M is an object in the subcategory C of the triangulated category T and X --> Y --> M --> is an Auslander-Reiten triangle in T, then there is an Auslander-Reiten triangle K --> L --> M --> in C if and only if there is a C-cover of the form K --> X. The main theorem is used to give a new proof of the existence of Auslander-Reiten sequences over finite dimensional algebras.
dc.description19 pages
dc.identifierhttps://arxiv.org/abs/math/0606647
dc.identifierhttp://arxiv.org/abs/math/0606647
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/114032
dc.subjectRepresentation Theory
dc.subjectRings and Algebras
dc.subject16G70, 18E30
dc.titleAuslander-Reiten triangles in subcategories
dc.typetext

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