Applied Categorical Structures

, Volume 19, Issue 5, pp 757–782 | Cite as

Perfect Derived Categories of Positively Graded DG Algebras

Article

Abstract

We investigate the perfect derived category \({{\rm dgPer}}(\mathcal{A})\) of a positively graded differential graded (dg) algebra \(\mathcal{A}\) whose degree zero part is a dg subalgebra and semisimple as a ring. We introduce an equivalent subcategory of \({{{\rm dgPer}}}(\mathcal{A})\) whose objects are easy to describe, define a t-structure on \({{{\rm dgPer}}}(\mathcal{A})\) and study its heart. We show that \({{{\rm dgPer}}}(\mathcal{A})\) is a Krull–Remak–Schmidt category. Then we consider the heart in the case that \(\mathcal{A}\) is a Koszul ring with differential zero satisfying some finiteness conditions.

Keywords

Differential graded module DG module t-structure Heart Koszul duality 

Mathematics Subject Classifications (2000)

18E30 16D90 

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© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Mathematisches InstitutUniversität BonnBonnGermany

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