Perfect Derived Categories of Positively Graded DG Algebras

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