Homology, Homotopy and Applications

Volume 21 (2019)

Number 2

Differential graded algebras over some reductive groups

Pages: 145 – 169

DOI: https://dx.doi.org/10.4310/HHA.2019.v21.n2.a9


Jin Cao (Yau Mathematical Sciences Center, Tsinghua University, Beijing, China)


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.


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

2010 Mathematics Subject Classification


Received 14 April 2017

Received revised 6 July 2018

Published 13 February 2019