2011/07/15 by Yiping Chen, Chen, Yiping
Mathematics · #FOS: Mathematics #Representation Theory (math.RT) #math.RT
paper · pdf · doi:10.48550/arxiv.1107.2985
19 pages. arXiv admin note: text overlap with arXiv:1102.2790
arxiv created 2012/04/08 · arxiv updated 2012/04/10
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, König 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.