On the correspondence between path algebras and generalized path algebras

Abstract The concept of generalized path algebras was introduced in Coelho and Liu (2000). It was shown in Ibáñez Cobos et al. (2008) how to obtain the Gabriel quiver of a given generalized path algebra. In this article, we generalize the concept of generalized path algebra to allow them to have relations, and we extend the result in Ibáñez Cobos et al. (2008) to this new setting. Moreover, we use the extended result mentioned above to address the inverse problem: that is, the problem of determining when a given algebra is isomorphic to a generalized path algebra in a non-trivial way.