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 SUq​(2) is described.Comment: 20 pages, no figures. Minor corrections in the example in Section 4