2009/12/31 by Ehud Meir, Meir, Ehud
Mathematics · #12G05 #16T20 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #math.QA #math.RA #msc:12G05 #msc:16T20
paper · pdf · doi:10.48550/arxiv.1001.0157
openalex publication_date 2009/12/31 · arxiv created 2011/12/16 · arxiv updated 2011/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that every central simple algebra A over a field k is Brauer equivalent to a quotient of a finite dimensional Hopf algebra over the same field (that is- A is Hopf Schur). If the characteristic of the field is zero, or if the algebra has a Galois splitting field of degree prime to the characteristic of k, we can take this Hopf algebra to be semisimple. We also show that if F is any finite extension of k, then F is a quotient of a finite dimensional Hopf algebra over k. We use it in order to show why the algebric closeness assumption is necessary in a weak form of Kaplansky's tenth conjecture, due to Stefan