dorsal/arxiv
View SchemaOn the algebraic structure of differential calculus on quantum groups
| Authors | O. V. Radko, A. A. Vladimirov |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9702020 |
| URL | https://arxiv.org/abs/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.
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"abstract": "Intrinsic Hopf algebra structure of the Woronowicz differential complex is\nshown to generate quite naturally a bicovariant algebra of four basic objects\nwithin a differential calculus on quantum groups -- coordinate functions,\ndifferential 1-forms, Lie derivatives, and inner derivations -- as the\ncross-product algebra of two mutually dual graded Hopf algebras. This\nconstruction, properly taking into account Hopf-algebraic properties of\nWoronowicz\u0027s bicovariant calculus, provides a direct proof of the Cartan\nidentity and of many other useful relations. A detailed comparison with other\napproaches is also given.",
"arxiv_id": "q-alg/9702020",
"authors": [
"O. V. Radko",
"A. A. Vladimirov"
],
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"q-alg",
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"doi": "10.1063/1.531952",
"title": "On the algebraic structure of differential calculus on quantum groups",
"url": "https://arxiv.org/abs/q-alg/9702020"
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