Cartan Calculus for Hopf Algebras and Quantum Groups
Abstract
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 leftinvariant vector fields and implicit commutation relations for a leftinvariant basis of 1forms.
 Publication:

arXiv eprints
 Pub Date:
 June 1993
 arXiv:
 arXiv:hepth/9306022
 Bibcode:
 1993hep.th....6022S
 Keywords:

 High Energy Physics  Theory;
 Mathematics  Quantum Algebra
 EPrint:
 15 pages (submitted to Comm. Math. Phys.)