2004/09/20 by Lars Kadison, Kadison, Lars, Burkhard Külshammer +1 · 2 citations
Mathematics · #11R32 #16L60 #20C15 #20L05 #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Quantum Algebra (math.QA) #math.GR #math.QA #msc:11R32 #msc:16L60 #msc:20C15 #msc:20L05
paper · pdf · doi:10.48550/arxiv.math/0409346
final version, 19 pages. to appear: Communications in Algebra
openalex publication_date 2004/09/20 · arxiv created 2006/01/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.