Mixed algebras and quivers related to cell complexes

In this paper we study finite dimensional algebras arising from categories of perverse sheaves on finite regular cell complexes (cellular perverse algebras). We prove that such algebras are quasi-hereditary and have finite global dimension. We discuss some restrictions, under which cellular perverse algebras are Koszul. We also study the relationship between Koszul duality functors in the derived categories of categories of graded and non-graded modules over an algebra and its quadratic dual.