Differential Geometry of Hopf Algebras and Quantum Groups.
Abstract
The differential geometry on a Hopf algebra is constructed, by using the basic axioms of Hopf algebras and noncommutative differential geometry. The space of generalized derivations on a Hopf algebra of functions is presented via the smash product, and used to define and discuss quantum Lie algebras and their properties. The Cartan calculus of the exterior derivative, Lie derivative, and inner derivation is found for both the universal and general differential calculi of an arbitrary Hopf algebra, and, by restricting to the quasitriangular case and using the numerical Rmatrix formalism, the aforementioned structures for quantum groups are determined.
 Publication:

Ph.D. Thesis
 Pub Date:
 1994
 arXiv:
 arXiv:hepth/9412153
 Bibcode:
 1994PhDT.......185W
 Keywords:

 Physics: Elementary Particles and High Energy; Mathematics;
 High Energy Physics  Theory;
 Mathematics  Quantum Algebra
 EPrint:
 91 pages in LaTeX, uses American Mathematical Society symbols style file "amssymbols.sty"