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arXiv · 1408.6215

Classification of bicovariant differential calculi over free orthogonal Hopf algebras

Manon Thibault De Chanvalon
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Abstract

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.

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BibTeXRIS

Manon Thibault De Chanvalon. 2014-08-26. Classification of bicovariant differential calculi over free orthogonal Hopf algebras. https://arxiv.org/abs/1408.6215

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