Nearly Frobenius structures in some families of algebras

Abstract

In this article we continue with the study started in Artenstein et al. (Algebras Represent Theory 18:339–367, 2015) of nearly Frobenius structures in some representative families of finite dimensional algebras, as radical square zero algebras, string algebras and toupie algebras. We prove that such radical square zero algebras with at least one path of length two are nearly Frobenius. As for the string algebras, those who are not gentle can be endowed with at least one non-trivial nearly Frobenius structure. Finally, in the case of toupie algebras, we prove that the existence of monomial relations is a sufficient condition to have non-trivial nearly Frobenius structures. Using the technics developed for the previous families of algebras we prove sufficient conditions for the existence of non-trivial Frobenius structures in quotients of path algebras in general.