Cokernels of the Cartan matrix and stratifying systems

We study the cokernel of the application given by the Cartan matrix C of a finite dimensional k-algebra This produces a finitely generated abelian group, the Cartan group which is invariant under derived equivalences. We are interested in the case when G is finite. For a standardly stratified algebra, it is shown that this group is always finite and some interesting connections with the standard modules are found. As a consequence, it is got that G can be seen as a measure of how far is a standardly stratified algebra to be quasi-hereditary. Finally, it is also shown that any finite abelian group can be realized as the Cartan group of some standardly stratified algebra.