The Space of Vector Fields on Q-Groups

1993/11/25 by Paolo Aschieri, P. Aschieri, Aschieri, P.
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th

paper · pdf · doi:10.48550/arxiv.hep-th/9311151

LATEX FILE,16 pages November 1993 UCLA/93/TEP/25

arxiv created 1993/11/25 · openalex publication_date 1993/11/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Related

• Realization of Vector fields for Quantum Groups as Pseudodifferential Operators on Quantum Spaces
• Quantum Groups, Non-Commutative Differential Geometry and Applications
• Cartan Calculus for Hopf Algebras and Quantum Groups
• Lectures on Hopf Algebras, Quantum Groups and Twists
• Quantum Group Sheaf and Quantum Manifolds