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Depth two, normality and a trace ideal condition for Frobenius extensions

Lars Kadison·Burkhard Külshammer
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Abstract

We review the depth two and Hopf algebroid-Galois theory in math.RA/0108067 and specialize to induced representations of semisimple algebras and character theory of finite groups. We show that depth two subgroups over the complex numbers are normal subgroups. As a converse we observe that normal Hopf subalgebras over a field are depth two extensions. We introduce a generalized Miyashita-Ulbrich action on the centralizer of a ring extension, and apply it to a study of depth two and separable extensions, providing new characterizations of separable and H-separable extensions. With a view to the problem of when separable extensions are Frobenius, we supply a trace ideal condition for when a ring extension is Frobenius.

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Lars Kadison, Burkhard Külshammer. 2006-01-20. Depth two, normality and a trace ideal condition for Frobenius extensions. https://arxiv.org/abs/math/0409346

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