Isomorphisms of graded path algebras

TL;DR

This paper proves that algebra isomorphisms between graded path algebras with homogeneous relations imply graded isomorphisms, extending previous results to a broader class of algebras.

Contribution

It generalizes Bell and Zhang's result from connected to possibly disconnected graded path algebras, establishing isomorphism equivalence.

Findings

Algebra isomorphisms imply graded isomorphisms for these algebras

Extension of previous connected case results

Broader applicability to graded path algebras

Abstract

We prove that if two path algebras with homogeneous relations are isomorphic as algebras, then they are isomorphic as graded path algebras. This extends a result by Bell and Zhang in the connected case.