Cartan Calculus: Differential Geometry for Quantum Groups

Details Cartan Calculus: Differential Geometry for Quantum Groups Cartan Calculus: Differential Geometry for Quantum Groups

1994-08-30

arxiv.org/abs/hep-th/9408170v1

Physics

High Energy Physics

High Energy Physics - Theory

17 pages. Lecture, Enrico Fermi Summer School

Scientific paper

A rigid framework for the Cartan calculus of Lie derivatives, inner derivations, functions, and forms is proposed. The construction employs a semi-direct product of two graded Hopf algebras, the respective super-extensions of the deformed universal enveloping algebra and the algebra of functions on a quantum group. Relations in the Cartan calculus follow as consistency conditions. The approach is not a priori based on the Leibniz rule for the exterior derivative and might hence also be of interest in the recent work on its deformations. The Cartan identity for the Lie derivatives is proven. (This article is based on a lecture given at the Enrico Fermi Summer School on Quantum Groups, Varenna, June 1994)

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