On the algebraic structure of differential calculus on quantum groups

Abstract

Intrinsic Hopf algebra structure of the Woronowicz differential complex is shown to generate quite naturally a bicovariant algebra of four basic objects within a differential calculus on quantum groups -- coordinate functions, differential 1-forms, Lie derivatives, and inner derivations -- as the cross-product algebra of two mutually dual graded Hopf algebras. This construction, properly taking into account Hopf-algebraic properties of Woronowicz's bicovariant calculus, provides a direct proof of the Cartan identity and of many other useful relations. A detailed comparison with other approaches is also given.

14 pages, LaTeX 2.09, no figures, JINR preprint

References in corpus (5)

• Vector Fields on Quantum Groups
• On Quantum Lie Algebras and Quantum Root Systems
• Quantum Double and Differential Calculi
• Poincare'-Birkhoff-Witt property for bicovariant differential algebras on simple quantum groups
• Implications of the Hopf algebra properties of noncommutative differential calculi

Cited by in corpus (7)

• Quantum kappa-deformed differential geometry and field theory
• Standard Complex for Quantum Lie Algebras
• Differential Calculus in Braided Abelian Categories
• Realization of bicovariant differential calculus on the Lie algebra type noncommutative spaces
• Generalization of Weyl realization to a class of Lie superalgebras
• T-Minkowski noncommutative spacetimes II: classical field theory
• The quantum Cartan algebra associated to a bicovariant differential calculus