A Hopf algebra having a separable Galois extension is finite dimensional

Cuadra, Juan

doi:10.1090/S0002-9939-08-09557-9

A Hopf algebra having a separable Galois extension is finite dimensional
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Proc. Amer. Math. Soc. 136 (2008), 3405-3408 Request permission

Abstract:

It is shown that a Hopf algebra $H$ over a field admitting a Galois extension $A$ separable over its subalgebra of coinvariants $B$ is of finite dimension. This answers in the affirmative a question posed by Beattie et al. in [Proc. Amer. Math. Soc. 128, No. 11 (2000), 3201-3203]. It is also proven that this result holds true if $H$ has bijective antipode and the extension $A/B$ is Frobenius.

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