Galois covering and smash product of skew categories

Abstract

In this paper we give a new proof of the famous result of E. L. Green [3], that gradings of a finite, path connected quiver are in one-to-one correspondence with Galois coverings. Namely we prove that the inverse construction to the skew group construction has as many solutions as the number of different gradings on the starting quiver.

Keywords

• smash product
• galois covering
• skew group algebras