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Derived equivalences from cohomological approximations and mutations of Φ-Yoneda algebras

Published online by Cambridge University Press:  22 May 2013

Wei Hu ,
Steffen Koenig  and
Changchang Xi
Wei Hu
Affiliation:
School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Beijing Normal University, 100875 Beijing, People's Republic of China
Steffen Koenig
Affiliation:
Institut für Algebra and Zahlentheorie, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
Changchang Xi
Affiliation:
School of Mathematical Sciences, Capital Normal University, 100048 Beijing, People's Republic of China ([email protected])
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Abstract

A new construction of derived equivalences is given, which relates different endomorphism rings and, more generally, cohomological endomorphism rings, including higher extensions, of objects in triangulated categories. These objects need to be connected by certain universal maps that are cohomological approximations and that exist in very general circumstances. The construction turns out to be applicable to a wide variety of situations, covering finite-dimensional algebras as well as certain infinite-dimensional algebras, Frobenius categories and n-Calabi–Yau categories.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 143 , Issue 3 , June 2013 , pp. 589 - 629
Copyright
Copyright © Royal Society of Edinburgh 2013 

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