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Derived invariance by syzygy complexes

Published online by Cambridge University Press:  13 February 2017

JIAQUN WEI
JIAQUN WEI*
Affiliation:
Institute of Mathematics, School of Mathematics Sciences, Nanjing Normal University, Nanjing 210023, P.R. China. e-mail: weijiaqun@njnu.edu.cn
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Abstract

We study derived invariance through syzygy complexes. In particular, we prove that syzygy-finite algebras and Igusa--Todorov algebras are invariant under derived equivalences. Consequently, we obtain that both classes of algebras are invariant under tilting equivalences. We also prove that derived equivalences preserve AC-algebras and the validity of the finitistic Auslander conjecture.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 164 , Issue 2 , March 2018 , pp. 325 - 343
Copyright
Copyright © Cambridge Philosophical Society 2017 

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