Bicovariant differential geometry of the quantum group GL_q(3)

Abstract

We construct a bicovariant differential calculus on the quantum group $G{L}_q(3)$, 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 $G{L}_q(3)$ are given explicitly.

16 p., LaTeX, DFTT-44/92

References in corpus (5)

• Quantum group gauge theory on quantum spaces
• An introduction to non-commutative differential geometry on quantum groups
• Differential Geometry on Linear Quantum Groups
• Gauge theories of quantum groups
• Bicovariant Differential Calculus on the Quantum D=2 Poincare Group

Cited by in corpus (5)

• On Quantum Lie Algebras and Quantum Root Systems
• $S{U}_3$ coherent state operators and invariant correlation functions and their quantum group counterparts
• Classification of bicovariant differential calculi on the Jordanian quantum groups GL_{g,h}(2) and SL_{h}(2) and quantum Lie algebras
• All bicovariant differential calculi on Glq(3,C) and SLq(3,C)
• Differential calculus on quantum groups: Constructive procedure