Frobenius structural matrix algebras. (Q2435526)

The goal of the paper is to characterize when the incidence coalgebra of a locally finite preordered set is co-Frobenius. It turns out this is the case if, and only if the incidence coalgebra is cosemisimple. As an application the authors characterize when a structural matrix algebra (i.e., a subalgebra of the algebra of all quadratic matrices of fixed finite size over a field which have zeros at certain prescribed positions) is a Frobenius algebra.