A Class of Bicovariant Differential Calculi on Hopf Algebras

Abstract

We introduce a large class of bicovariant differential calculi on any quantum group $A$, associated to $Ad$-invariant elements. For example, the deformed trace element on $S{L}_q(2)$ recovers Woronowicz' $4D_{\pm }$ calculus. More generally, we obtain a sequence of differential calculi on each quantum group $A(R)$, based on the theory of the corresponding braided groups $B(R)$. Here $R$ is any regular solution of the QYBE.

16 pages

References in corpus (2)

• Differential Geometry on Linear Quantum Groups
• Quantum and Braided Linear Algebra

Cited by in corpus (5)

• Quantum Group Gauge Theories and Covariant Quantum Algebras
• Z${}_3$-graded differential geometry of quantum plane
• Quantum group covariant noncommutative geometry
• Integrals in Hopf algebras over rings
• A quantum homogeneous space of nilpotent matrices