Forms of certain hopf algebras |
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Authors: | David E Radford Earl J Taft Robert Lee Wilson |
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Institution: | 1. Department of Mathematics, Lawrence University, 54911, Appleton, Wisconsin, USA 2. Department of Mathematics, Rutgers University, 08903, New Brunswick, New Jersey, USA
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Abstract: | Let Ψ be a field, G a finite group of automorphisms of Ψ, and Φ the fixed field of G. Let H be a Hopf algebra over Ψ. For g ∈ G we define a Hopf algebra Hg which has the same underlying vector space as H and modified operations and show that the tensor product (over Ψ) ?g ∈ G Hg has a Φ-form. As a consequence we see that if n>0 is an integer and Φ is a field of characteristic zero or p>0 with (n,p)=1, then there is a finite dimensional Hopf algebra over Φ with antipode of order 2n. |
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