Abstract
For a polynomial algebra \(A = R\left[ X \right]{\text{ or }}R\left[ {X,X^{ - 1} } \right]\) in several variables over a commutative ring R with a Hopf algebra structure \(\left( {A,m,e,\Delta ,\varepsilon ,S} \right)\) the existence of the dual Hopf algebra \(\left( {A^\circ ,\Delta ^\circ ,\varepsilon ^\circ ,m^\circ ,e^\circ ,S^\circ } \right)\) is proved.
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Kurakin, V.L. Hopf Algebra Dual to a Polynomial Algebra over a Commutative Ring. Mathematical Notes 71, 617–623 (2002). https://doi.org/10.1023/A:1015879619768
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DOI: https://doi.org/10.1023/A:1015879619768