From Quantum Planes to Quantum Groups and back; Cartan Calculus
High Energy Physics - Theory
2008-02-03 v1 Quantum Algebra
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.
Cite
@article{arxiv.hep-th/9312076,
title = {From Quantum Planes to Quantum Groups and back; Cartan Calculus},
author = {Peter Schupp},
journal= {arXiv preprint arXiv:hep-th/9312076},
year = {2008}
}
Comments
49 pages