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

Abstract

We discuss the algebra of $N\times N$ matrices as a reduced quantum plane. A $3-$nilpotent deformed differential calculus involving a complex parameter $q$ is constructed. The two cases, $q$ $3^{rd}$ and $N^{th}$ root of unity are completely treated. As application, a gauge field theory for the particular cases $n=2$ and $n=3$ is established.

References in corpus (2)

• Enveloping algebra valued gauge transformations for non-abelian gauge groups on non-commutative spaces
• Noncommutative gauge theory for Poisson manifolds

Cited by in corpus (1)

• n=3 Nilpotent differential calculus on some non-commutative (super) spaces