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Classification of Bicovariant Differential Calculi over free Orthogonal Hopf Algebras

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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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  1. Laboratoire de Mathématiques (UMR 6620), Université Blaise Pascal de Clermont-Ferrand, Complexe universitaire des Cézeaux, 63171, Aubière Cedex, France

    Manon Thibault de Chanvalon

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  1. Manon Thibault de Chanvalon
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Correspondence to Manon Thibault de Chanvalon.

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Presented by Michel Van den Bergh.

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Thibault de Chanvalon, M. Classification of Bicovariant Differential Calculi over free Orthogonal Hopf Algebras. Algebr Represent Theor 18, 831–847 (2015). https://doi.org/10.1007/s10468-015-9518-y

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