Differential graded algebras over some reductive groups

In this paper, we study the general properties of commutative differential graded algebras in the category of representations over a reductive algebraic group with an injective central cocharacter. Besides describing the derived category of differential graded modules over such an algebra, we also provide a criterion for the existence of a $t$-structure on the derived category together with a characterization of the coordinate ring of the Tannakian fundamental group of its heart.

Keywords

rational homotopy theory, graded differential algebra, reductive group, Tannakian category, Hopf algebra

2010 Mathematics Subject Classification

18D35

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Received 14 April 2017

Received revised 6 July 2018

Published 13 February 2019