Resumen
- 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 HC 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 Hmod(R) and HC interact via various functors. If C is functorially finite then HC is a quotient category of Hmod(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 HC correspond to Iyama's higher AR sequences and derive his higher AR duality from the existence of a Serre functor on the derived category Db(HC).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.