n=3 diferential calculus on a given reduced quantum plane and gauge theory

Abstract

We discuss the algebra of $N\times N$ matrices that seems to be as a reduced quantum plane. A new deformed differential calculus involving a complex parameter $q$ is introduced. The two cases, $q$ generic and $q$ $N-$th root of unity are completely treated. As an application, we give a connection with gauge field theory for the particular cases $n=2$ and $n=3.