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Approximations, ghosts and derived equivalences

Part of: Abelian groups Representation theory of rings and algebras Abelian categories Homological algebra

Published online by Cambridge University Press:  26 January 2019

Yiping Chen  and
Wei Hu
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)
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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.

Keywords

derived equivalencemutationghost idealtilting complex

MSC classification

Primary: 18E30: Derived categories, triangulated categories 20K40: Homological and categorical methods
Secondary: 18G35: Chain complexes 16G10: Representations of Artinian rings
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 150 , Issue 2 , April 2020 , pp. 813 - 840
Copyright
Copyright © Royal Society of Edinburgh 2019

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