VECTOR FIELDS ON QUANTUM GROUPS

1995/05/18 by Paolo Aschieri, Peter Schupp
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #hep-th #math.QA #q-alg

paper · pdf · doi:10.1142/s0217751x9600050x

published as Int.J.Mod.Phys. A11 (1996) 1077-1100 · 25 pages, latex, uses bezier.sty

arxiv created 1995/05/18 · openalex publication_date 1996/03/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

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 one-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.

Citations

• Cartan Calculus: Differential Geometry for Quantum Groups
• Quantum Groups, Non-Commutative Differential Geometry and Applications
• Universal and Generalized Cartan Calculus on Hopf Algebras
• Differential calculus on compact matrix pseudogroups (quantum groups)