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.

Keywords:

• Bound path algebras
• generalized path algebras
• representations of algebras

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 16G10
• Secondary: 16G20

Additional information

Funding

This paper was written while the first named author was a graduate student under the supervision of the second. The authors gratefully acknowledge financial support by São Paulo Research Foundation (FAPESP), grant #2018/18123-5. The second author has also a grant by CNPq (Pq 312590/2020-2).