I asked this question in mathoverflow. But it was closed. So I ask it here.
If we have a complete set of primitive orthogonal idempotents of an algebra $A$, then we can obtain simple modules, indecomposable projective modules, indecomposable injective modules of $A$.
If we obtain a complete set of primitive central idempotents of $A$, what modules can be obtain?
I found that some papers compute a complete set of primitive orthogonal idempotents of an algebra while some other papers compute primitive central idempotents. What are the differences between primitive central idempotents and primitive orthogonal idempotents? Thank you very much.