Laura Năstăsescu
Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucharest, Romania

We start with two matrix coalgebras $\mathcal{E}$ and $\mathcal{F}$, and then we adjoint two families of elements which in a matrix formal way behave like some kind of skew-primitives with respect to $\mathcal{E}$ and $\mathcal{F}$. In this way we construct in a natural way a class of finite dimensional coalgebras. We show that the obtained coalgebras are quasi-co-Frobenius and are co-Frobenius only when $\mathcal{E}$ and $\mathcal{F}$ have the same size. By taking the dual algebras, we obtain a large class of quasi-Frobenius algebras which are not Frobenius.