On the algebraic structure of differential calculus on quantum groups
arXiv:q-alg/9702020 · doi:10.1063/1.531952
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
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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