Classification of bicovariant differential calculi over free orthogonal Hopf algebras

Manon Thibault de Chanvalon (1)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal

We show that if two Hopf algebras are monoidally equivalent, then their categories of bicovariant differential calculi are equivalent. We then classify, for $q \in \mathbb{C}^*$ not a root of unity, the finite dimensional bicovariant differential calculi over the Hopf algebra $\mathcal{O}_q(SL_2)$. Using a monoidal equivalence between free orthogonal Hopf algebras and $\mathcal{O}_q(SL_2)$ for a given $q$, this leads us to the classification of finite dimensional bicovariant differential calculi over free orthogonal Hopf algebras.

Mots clés: quantum groups; bicovariant differential calculus; Yetter-Drinfeld modules

Domaines: Algèbres quantiques [math.QA]

Manon Thibault de Chanvalon. Classification of bicovariant differential calculi over free orthogonal Hopf algebras. 2014. ⟨hal-01058446⟩