On the algebraic structure of differential calculus on quantum groups

O. V. Radko; A. A. Vladimirov

doi:10.1063/1.531952

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On the algebraic structure of differential calculus on quantum groups

O. V. Radko·A. A. Vladimirov

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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.

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O. V. Radko, A. A. Vladimirov. 1997-02-14. On the algebraic structure of differential calculus on quantum groups. https://doi.org/10.1063/1.531952

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