Vector Fields on Quantum Groups

Abstract

We construct the space of vector fields on a generic quantum group. Its elements are products of elements of the quantum group itself with left invariant vector fields. We study the duality between vector fields and 1-forms and generalize the construction to tensor fields. A Lie derivative along any (also non left invariant) vector field is proposed and a puzzling ambiguity in its definition discussed. These results hold for a generic Hopf algebra.

25 pages, latex, uses bezier.sty

References in corpus (3)

• Cartan Calculus: Differential Geometry for Quantum Groups
• Universal and Generalized Cartan Calculus on Hopf Algebras
• Quantum Groups, Non-Commutative Differential Geometry and Applications

Cited by in corpus (16)

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• Universal Enveloping Algebra and Differential Calculi on Orthogonal q-groups
• Finite group discretization of Yang-Mills and Einstein actions
• The Problem of Differential Calculus on Quantum Groups
• On the Geometry of the Quantum Poincare Group
• Quantised ${\mathfrak{sl}}_2$-differential algebras
• Hopf modules and their duals
• The quantum Cartan algebra associated to a bicovariant differential calculus
• Quantum Calculi: differential forms and vector fields in noncommutative geometry
• On 2d gravity and parallel transport field equation on quantum sphere
• Drinfeld-Jimbo quantum Lie algebra