Bicovariant differential geometry of the quantum group GL_q(3)

TL;DR

This paper develops a bicovariant differential calculus for the quantum group GL_q(3), providing explicit formulas and extending to its restriction involving SU(3) and U(1).

Contribution

It introduces a new bicovariant differential calculus on GL_q(3) and derives the associated Lie algebra, Cartan-Maurer equations, and non-commutative geometric quantities.

Findings

Explicit construction of bicovariant differential calculus on GL_q(3)

Derivation of the q-Lie algebra and Cartan-Maurer equations

Explicit expressions for non-commutative geometric quantities

Abstract

We construct a bicovariant differential calculus on the quantum group $GL_q(3)$, and discuss its restriction to $[SU(3) \otimes U(1)]_q$. The $q$-algebra of Lie derivatives is found, as well as the Cartan-Maurer equations. All the quantities characterizing the non-commutative geometry of $GL_q(3)$ are given explicitly.