Differential Geometry on Hopf Algebras and Quantum Groups (Ph.D. Thesis)

Details Differential Geometry on Hopf Algebras and Quantum Groups (Ph.D. Thesis) Differential Geometry on Hopf Algebras and Quantum Groups (Ph.D. Thesis)

1994-12-17

arxiv.org/abs/hep-th/9412153v1

Physics

High Energy Physics

High Energy Physics - Theory

91 pages in LaTeX, uses American Mathematical Society symbols style file "amssymbols.sty"

Scientific paper

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 R-matrix formalism, the aforementioned structures for quantum groups are determined.

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