Strongly simply connected schurian algebras and multiplicative bases

Abstract

In this paper, we define concepts of crowns and quasi-crowns, valid in an arbitrary schurian algebra, and which generalise the corresponding concepts in an incidence algebra. We show first that a triangular schurian algebra is strongly simply connected if and only if it is simply connected and contains no quasi-crown. We then prove that the absence of quasi-crowns in a triangular schurian algebra implies the existence of a multiplicative basis.