Oriented CW complexes and finite‐dimensional alternative algebras

Abstract

In this paper, a link between oriented CW complexes (that will also be mentioned as configurations) and alternative algebras is studied, determining which configurations are associated with those algebras. Moreover, the isomorphism classes of each two‐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 algebra is alternative, while the second one constructs and draws the (pseudo)digraph associated with a given alternative algebra.