Cartan Calculus on Quantum Lie Algebras

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 spaces we combine an exterior derivative, inner derivations, Lie derivatives, forms and functions all into one big algebra, the “Cartan Calculus”. (This is an extended version of a talk presented by P. Schupp at the XXII International Conference on Differential Geometric Methods in Theoretical Physics, Ixtapa, Mexico, September 1993) This work was supported in part by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DE-AC03-76SF00098 and in part by the National Science Foundation under grant PHY-90-21139. [email protected] [email protected]