From Quantum Planes to Quantum Groups and back; Cartan Calculus
Abstract
A Cartan Calculus of Lie derivatives, differential forms, and inner derivations, based on an undeformed Cartan identity, is constructed. We attempt a classification of various types of quantum Lie algebras and present a fairly general example for their construction, utilizing pure braid methods, proving orthogonality of the adjoint representation and giving a (Killing) metric and the quadratic casimir. A reformulation of the Cartan calculus as a braided algebra and its extension to quantum planes, directly and induced from the group calculus, are provided.
 Publication:

arXiv eprints
 Pub Date:
 December 1993
 arXiv:
 arXiv:hepth/9312076
 Bibcode:
 1993hep.th...12076S
 Keywords:

 High Energy Physics  Theory;
 Mathematics  Quantum Algebra
 EPrint:
 49 pages