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Silting mutation in triangulated categories

Aihara, Takuma ; Iyama, Osamu

Journal of the London Mathematical Society, 2012-06, Vol.85 (3), p.633-668 [Periódico revisado por pares]

Oxford University Press

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  • Título:
    Silting mutation in triangulated categories
  • Autor: Aihara, Takuma ; Iyama, Osamu
  • Assuntos: Algebra ; Categories ; Clusters ; Mathematical analysis ; Mutations ; Representations
  • É parte de: Journal of the London Mathematical Society, 2012-06, Vol.85 (3), p.633-668
  • Notas: 18E30 (primary), 16E30 (secondary). The second author was supported by JSPS Grant‐in‐Aid for Scientific Research 21740010, 21340003, 20244001 and 22224001.
    2010
    Mathematics Subject Classification
    ObjectType-Article-1
    SourceType-Scholarly Journals-1
    ObjectType-Feature-2
    content type line 23
  • Descrição: In representation theory of algebras the notion of ‘mutation’ often plays important roles, and two cases are well known, that is, ‘cluster tilting mutation’ and ‘exceptional mutation’. In this paper we focus on ‘tilting mutation’, which has a disadvantage that it is often impossible, that is, some of summands of a tilting object cannot be replaced to get a new tilting object. The aim of this paper is to take away this disadvantage by introducing ‘silting mutation’ for silting objects as a generalization of ‘tilting mutation’. We shall develop a basic theory of silting mutation. In particular, we introduce a partial order on the set of silting objects and establish the relationship with ‘silting mutation’ by generalizing the theory of Riedtmann–Schofield and Happel–Unger. We show that iterated silting mutations act transitively on the set of silting objects for local, hereditary or canonical algebras. Finally, we give a bijection between silting subcategories and certain t‐structures.
  • Editor: Oxford University Press
  • Idioma: Inglês
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  • Realização: ABCD-USP USP   Logos de Redes Sociais: Freepik

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