Higher Auslander-Reiten sequences and t-structures

JOURNAL OF ALGEBRA

卷:459

Article

Arias, Juan Camilo¹  Backelin, Erik¹ 

[1] Univ Los Andes, Carrera 1 18A-10, Bogota, Colombia

关键词: t-Structure;    Auslander Reiten sequence;    Category O;   

DOI  :  10.1016/j.jalgebra.2016.03.040

来源: Elsevier

【 摘 要 】

Let R be an artin algebra and C an additive subcategory of mod(R). We construct a t-structure on the homotopy category K-(C) and argue that its heart H-c is a natural domain for higher Auslander-Reiten (AR) theory. In the paper [5] we showed that K- (mod(R)) is a natural domain for classical AR theory. Here we show that the abelian categories H-mod(R) and H-c interact via various functors. If C is functorially finite then H-c is a quotient category of H-mod(R). We illustrate our theory with two examples: When C is a maximal n-orthogonal subcategory Iyama developed a higher AR theory, see [10]. In this case we show that the simple objects of H-c correspond to Iyama's higher AR sequences and derive his higher AR duality from the existence of a Serre functor on the derived category D-b(H-c). The category O of a complex semi-simple Lie algebra fits into higher AR theory in the situation when R is the coinvariant algebra of the Weyl group. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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