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DIFFERENTIAL GRADED ENDOMORPHISM ALGEBRAS, COHOMOLOGY RINGS AND DERIVED EQUIVALENCES

Part of: Homological algebra Abelian categories Representation theory of rings and algebras Rings and algebras arising under various constructions

Published online by Cambridge University Press:  12 September 2018

SHENGYONG PAN ,
ZHEN PENG  and
JIE ZHANG
SHENGYONG PAN*
Affiliation:
Department of Mathematics, Beijing Jiaotong University, Beijing 100044, ChinaBeijing Center for Mathematics and Information Interdisciplinary Sciences, Beijing 100048, China e-mail: shypan@bjtu.edu.cn
ZHEN PENG*
Affiliation:
School of Mathematics and Statistics, Anyang Normal University, Anyang 455000, China e-mail: pzhen2002@163.com
JIE ZHANG*
Affiliation:
Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China e-mail: jiezhang@bit.edu.cn
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Abstract

In this paper, we will consider derived equivalences for differential graded endomorphism algebras by Keller's approaches. First, we construct derived equivalences of differential graded algebras which are endomorphism algebras of the objects from a triangle in the homotopy category of differential graded algebras. We also obtain derived equivalences of differential graded endomorphism algebras from a standard derived equivalence of finite dimensional algebras. Moreover, under some conditions, the cohomology rings of these differential graded endomorphism algebras are also derived equivalent. Then we give an affirmative answer to a problem of Dugas (A construction of derived equivalent pairs of symmetric algebras, Proc. Amer. Math. Soc. 143 (2015), 2281–2300) in some special case.

MSC classification

Primary: 18E30: Derived categories, triangulated categories
Secondary: 16G10: Representations of Artinian rings 16S10: Rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) 18G15: Ext and Tor, generalizations, Künneth formula
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 61 , Issue 3 , September 2019 , pp. 557 - 573
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

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References

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