Implications of the Hopf algebra properties of noncommutative differential calculi

Abstract

We define a noncommutative algebra of four basic objects within a differential calculus on quantum groups: functions, 1-forms, Lie derivatives and inner derivations, as the cross-product algebra associated with Woronowicz's (differential) algebra of functions and forms. This definition properly takes into account the Hopf algebra structure of the Woronowicz calculus. It also provides a direct proof of the Cartan identity.

4 pages, LaTeX 2.09, no figures, contributed to the Proceedings of the 5th Colloquium on "Quantum Groups and Integrable Systems", Prague, June 1996 (to appear in Czech.J.Phys)

References in corpus (3)

• An introduction to non-commutative differential geometry on quantum groups
• Differential Geometry on Linear Quantum Groups
• Bicovariant Quantum Algebras and Quantum Lie Algebras

Cited by in corpus (2)

• On the algebraic structure of differential calculus on quantum groups
• Differential Calculus in Braided Abelian Categories