Derived equivalences in n-angulated categories

Yiping Chen

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arXiv · 1107.2985

Derived equivalences in n-angulated categories

Yiping Chen

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Abstract

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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BibTeX RIS

Yiping Chen. 2011-07-15. Derived equivalences in n-angulated categories. https://arxiv.org/abs/1107.2985

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