Derived equivalences in n-angulated categories

Details Derived equivalences in n-angulated categories Derived equivalences in n-angulated categories

2011-07-15

arxiv.org/abs/1107.2985v2

Mathematics

Representation Theory

19 pages. arXiv admin note: text overlap with arXiv:1102.2790

Scientific paper

In this paper, we consider $n$-perforated Yoneda algebras for $n$-angulated categories, and show that, under some conditions, $n$-angles induce derived equivalences between the quotient algebras of $n$-perforated Yoneda algebras. This result generalizes some results of Hu, K\"{o}nig and Xi. And it also establishes a connection between higher cluster theory and derived equivalences. Namely, in a cluster tilting subcategory of a triangulated category, an Auslander-Reiten $n$-angle implies a derived equivalence between two quotient algebras. This result can be compared with the fact that an Auslander-Reiten sequence suggests a derived equivalence between two algebras which was proved by Hu and Xi.

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