On the algebraic structure of differential calculus on quantum groups

Details On the algebraic structure of differential calculus on quantum groups On the algebraic structure of differential calculus on quantum groups

1997-02-14

arxiv.org/abs/q-alg/9702020v1

Mathematics

Quantum Algebra

14 pages, LaTeX 2.09, no figures, JINR preprint

Scientific paper

10.1063/1.531952

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.

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