Cartan Calculus for Hopf Algebras and Quantum Groups

Details Cartan Calculus for Hopf Algebras and Quantum Groups Cartan Calculus for Hopf Algebras and Quantum Groups

1993-06-03

arxiv.org/abs/hep-th/9306022v1

Physics

High Energy Physics

High Energy Physics - Theory

15 pages (submitted to Comm. Math. Phys.)

Scientific paper

A generalization of the differential geometry of forms and vector fields to the case of quantum Lie algebras is given. In an abstract formulation that incorporates many existing examples of differential geometry on quantum groups, we combine an exterior derivative, inner derivations, Lie derivatives, forms and functions all into one big algebra. In particular we find a generalized Cartan identity that holds on the whole quantum universal enveloping algebra of the left-invariant vector fields and implicit commutation relations for a left-invariant basis of 1-forms.

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