The quantum Cartan algebra associated to a bicovariant differential calculus

Abstract

We associate to any (suitable) bicovariant differential calculus on a quantum group a Cartan Hopf algebra which has a left, respectively right, representation in terms of left, respectively right, Cartan calculus operators. The example of the Hopf algebra associated to the $4D_{+}$ differential calculus on $S{U}_q(2)$ is described.

20 pages, no figures. Minor corrections in the example in Section 4.

References in corpus (2)

• Vector Fields on Quantum Groups
• On the algebraic structure of differential calculus on quantum groups