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Approximations, ghosts and derived equivalences

Published online by Cambridge University Press:  26 January 2019

Yiping Chen
Affiliation:
School of Mathematics and Statistics, Wuhan University, Wuhan, 430072China (ypchen@whu.edu.cn)
Wei Hu
Affiliation:
School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing, 100875China (huwei@bnu.edu.cn)
Corresponding

Abstract

Approximation sequences and derived equivalences occur frequently in the research of mutation of tilting objects in representation theory, algebraic geometry and noncommutative geometry. In this paper, we introduce symmetric approximation sequences in additive categories and weakly n-angulated categories which include (higher) Auslander-Reiten sequences (triangles) and mutation sequences in algebra and geometry, and show that such sequences always give rise to derived equivalences between the quotient rings of endomorphism rings of objects in the sequences modulo some ghost and coghost ideals.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2019

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