Let A be a positively graded algebra such that A_0 has finite global dimension (see "On a common generalization of Koszul duality and tilting equivalence" by Dag Madsen, arXiv.org > math > arXiv:1007.3282)
I am not an expert in this kind of algebras but is it true that, like in the classical case of Koszul algebras, the generalized Koszul algebras are of finite global dimension?
In the classical case where A_0 is semisimple (or of global dimension zero) we have that the global dimension of A is finite.
What happens in the generalized case? Does the same property hold, namely that the global dimension of A is again finite?