## Abstract

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 Hmod(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.

Original language | English (US) |
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Pages (from-to) | 280-308 |

Number of pages | 29 |

Journal | Journal of Algebra |

Volume | 459 |

DOIs | |

State | Published - Aug 1 2016 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Algebra and Number Theory