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Depth two, normality and a trace ideal condition for Frobenius extensions | | Lars Kadison
; Burkhard Külshammer
; | | Date: |
20 Sep 2004 | | Subject: | Group Theory; Quantum Algebra MSC-class: 11R32, 16L60, 20L05, 20C15 | math.GR math.QA | | 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. | | Source: | arXiv, math.GR/0409346 | | Services: | Forum | Review | PDF | Favorites | |
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