Biproducts and Two-cocycle Twists of Hopf Algebras
Biproducts and Two-cocycle Twists of Hopf Algebras
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Hopf 代数的副积和二同循环扭曲
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
H. Schneider
中科院分区：
文献类型：
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作者：
D. Radford;H. Schneider
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{Y}D ). We describe the bialgebras (R#H) op and (R#H) o explicitly as bi-products ( R^{underline {op} } # H^{op} ) and ( R^{underline o } # H^o ) respectively where ( R^{underline {op} } ) is a bialgebra in ( _{H^{op} }^{H^{op} } mathcal{Y}D ) and ( R^{underline o } ) is a bialgebra in ( _{H^o }^{H^o } mathcal{Y}D ). We use our results to describe two-cocycle twist bialgebra structures on the tensor product of bi-products.
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{Y}D ). We describe the bialgebras (R#H) op and (R#H) o explicitly as bi-products ( R^{underline {op} } # H^{op} ) and ( R^{underline o } # H^o ) respectively where ( R^{underline {op} } ) is a bialgebra in ( _{H^{op} }^{H^{op} } mathcal{Y}D ) and ( R^{underline o } ) is a bialgebra in ( _{H^o }^{H^o } mathcal{Y}D ). We use our results to describe two-cocycle twist bialgebra structures on the tensor product of bi-products.