New York Journal of Mathematics
Volume 20 (2014) 779-797


Alan Koch

Hopf Galois structures on primitive purely inseparable extensions

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Published: August 27, 2014
Keywords: Hopf algebras, Hopf Galois extensions, purely inseparable extensions
Subject: 16T05

Let L/K be a primitive purely inseparable extension of fields of characteristic p, [L : K] >p, p odd. It is well known that L/K is Hopf Galois for some Hopf algebra H, and it is suspected that L/K is Hopf Galois for numerous choices of H. We construct a family of K-Hopf algebras H for which L is an H-Galois object. For some choices of K we will exhibit an infinite number of such H. We provide some explicit examples of the dual, Hopf Galois, structure on L/K.

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Department of Mathematics, Agnes Scott College, 141 E. College Ave., Decatur, GA 30030, USA