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arXiv · 1610.08191

Cohomology rings, differential graded algebras and derived equivalences

Shengyong Pan·Zhen Peng·Jie Zhang
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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 \cite{Dugas2015} in some special case.

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BibTeXRIS

Shengyong Pan, Zhen Peng, Jie Zhang. 2018-05-08. Cohomology rings, differential graded algebras and derived equivalences. https://doi.org/10.1017/s0017089518000368.

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