Nearly Morita equivalences and rigid objects
| Autor: | Robert J. Marsh, Yann Palu |
|---|---|
| Přispěvatelé: | School of Mathematics - University of Leeds, University of Leeds, Université de Picardie Jules Verne (UPJV), Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352 (LAMFA), Université de Picardie Jules Verne (UPJV)-Centre National de la Recherche Scientifique (CNRS), School of Mathematics [Leeds] |
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
16G20 16E35 18E30 18E35 (Primary) 13F60 (Secondary) Functor Endomorphism [MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT] Triangulated category General Mathematics 010102 general mathematics Mathematics - Category Theory 01 natural sciences Mathematics::Category Theory 0103 physical sciences Morita therapy FOS: Mathematics Category Theory (math.CT) 010307 mathematical physics 0101 mathematics Equivalence (formal languages) Representation Theory (math.RT) [MATH]Mathematics [math] Mathematics::Representation Theory Simple module Mathematics - Representation Theory Mathematics |
| Zdroj: | Nagoya Mathematical Journal Nagoya Mathematical Journal, Duke University Press, 2017, 225, pp.64-99. ⟨10.1017/nmj.2016.27⟩ |
| ISSN: | 0027-7630 |
| Popis: | If T and T′ are two cluster-tilting objects of an acyclic cluster category related by a mutation, their endomorphism algebras are nearly-Morita equivalent (Buan et al., Cluster-tilted algebras, Trans. Amer. Math. Soc. 359(1) (2007), 323–332 (electronic)), that is, their module categories are equivalent “up to a simple module”. This result has been generalised by D. Yang, using a result of Plamondon, to any simple mutation of maximal rigid objects in a 2-Calabi–Yau triangulated category. In this paper, we investigate the more general case of any mutation of a (non-necessarily maximal) rigid object in a triangulated category with a Serre functor. In that setup, the endomorphism algebras might not be nearly-Morita equivalent and we obtain a weaker property that we call pseudo-Morita equivalence. Inspired by Buan and Marsh (From triangulated categories to module categories via localization II: calculus of fractions, J. Lond. Math. Soc. (2) 86(1) (2012), 152–170; From triangulated categories to module categories via localisation, Trans. Amer. Math. Soc. 365(6) (2013), 2845–2861), we also describe our result in terms of localizations. |
| Databáze: | OpenAIRE |
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