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Biproducts and Two-Cocycle Twists of Hopf Algebras

David E. Radford·Hans-Jürgen Schneider
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Abstract

Let $H$ be a Hopf algebra with bijective antipode over a field $k$ and suppose that $R{#}H$ is a bi-product. Then $R$ is a bialgebra in the Yetter--Drinfel'd category ${}_H^H{\mathcal YD}$. We describe the bialgebras $(R{#}H)^{op}$ and $(R{#}H)^o$ explicitly as bi-products $R^{\UOP}{#}H^{op}$ and $R^{\UO}{#}H^o$ respectively where $R^{\UOP}$ is a bialgebra in ${}^{H^{op}}_{H^{op}}{\mathcal YD}$ and $R^{\UO}$ is a bialgebra in ${}^{H^o}_{H^o}{\mathcal YD}$. We use our results to describe two-cocycle twist bialgebra structures on the tensor product of bi-products.

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David E. Radford, Hans-Jürgen Schneider. 2006-03-11. Biproducts and Two-Cocycle Twists of Hopf Algebras. https://arxiv.org/abs/math/0603267

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