CMMSE: Finite-dimensional flexible algebras and oriented CW complexes

Abstract

In this paper, we study a link between oriented CW complexes (also called configurations) and flexible algebras determining which configurations are associated with those algebras. Some important elements that can be read from the (pseudo)digraph that is associated with a flexible algebra are studied. Moreover, the isomorphism classes of each 2-dimensional configuration associated with these algebras is analyzed, providing a new method to classify them. In order to complement the theoretical study, two algorithmic methods are implemented: the first one checks if a given oriented CW complex is associated or not with a flexible algebra, while the second one constructs and draws the (pseudo)digraph associated with a given flexible algebra.