1992/07/26 by Paolo Aschieri, P. Aschieri, Leonardo Castellani +1 · 129 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #Connection (principal bundle) #Differential calculus #Differential form #Differential geometry #Geometry #Lie group #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Noncommutative quantum field theory #Physics #Pure mathematics #Quantum #Quantum differential calculus #Quantum gravity #Quantum group #Quantum mechanics #Quantum spacetime #hep-th #math.QA
paper · pdf · doi:10.1142/s0217751x93000692
published in International Journal of Modern Physics A 08(10), 1667-1706 (World Scientific) · 45 pages
arxiv created 1992/07/26 · openalex publication_date 1993/04/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We give a pedagogical introduction to the differential calculus on quantum groups by stressing at all stages the connection with the classical case (q→1 limit). The Lie derivative and the contraction operator on forms and tensor fields are found. A new, explicit form of the Cartan-Maurer equations is presented. The example of a bicovariant differential calculus on the quantum group GL q (2) is given in detail. The softening of a quantum group is considered, and we introduce q curvatures satisfying q Bianchi identities, a basic ingredient for the construction of q gravity and q gauge theories.