Higher Auslander–Reiten sequences and t-structures

Let R   be an artin algebra and CC an additive subcategory of mod(R)mod(R). We construct a t  -structure on the homotopy category K−(C)K−(C) and argue that its heart HCHC is a natural domain for higher Auslander–Reiten (AR) theory. In the paper [5] we showed that K−(mod(R))K−(mod(R)) is a natural domain for classical AR theory. Here we show that the abelian categories Hmod(R)Hmod(R) and HCHC interact via various functors. If CC is functorially finite then HCHC is a quotient category of Hmod(R)Hmod(R). We illustrate our theory with two examples:When CC is a maximal n-orthogonal subcategory Iyama developed a higher AR theory, see [10]. In this case we show that the simple objects of HCHC 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)Db(HC).The category OO 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.