Implications of the Hopf algebra properties of noncommutative differential calculi

Details Implications of the Hopf algebra properties of noncommutative differential calculi Implications of the Hopf algebra properties of noncommutative differential calculi

1996-09-05

arxiv.org/abs/q-alg/9609005v1

Mathematics

Quantum Algebra

4 pages, LaTeX 2.09, no figures, contributed to the Proceedings of the 5th Colloquium on "Quantum Groups and Integrable System

Scientific paper

10.1023/A:1021412632436

We define a noncommutative algebra of four basic objects within a differential calculus on quantum groups: functions, 1-forms, Lie derivatives and inner derivations, as the cross-product algebra associated with Woronowicz's (differential) algebra of functions and forms. This definition properly takes into account the Hopf algebra structure of the Woronowicz calculus. It also provides a direct proof of the Cartan identity.

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