2005/01/01 by Lars Kadison, Kadison, Lars
Mathematics · #16S40 #16W30 (13B05 #20L05 #81R50) #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #math.QA #math.RA #msc:16S40 #msc:16W30 #msc:20L05
paper · pdf · doi:10.48550/arxiv.math/0501008
9 pp, three sections in conference paper
arxiv created 2005/01/01 · arxiv updated 2009/12/01
In this note we reduce certain proofs in \citeKS, Karl, AMA to depth two quasibases from one side only. This minimalistic approach leads to a characterization of Galois extensions for finite projective bialgebroids without the Frobenius extension property: a proper algebra extension is a left T-Galois extension for some right finite projective left bialgebroid T over some algebra R if and only if it is of left depth two and left balanced. Exchanging left and right in this statement, we have also a characterization of right Galois extensions for left finite projective right bialgebroids. As a corollary, we obtain insights into split monic Galois mappings and endomorphism ring theorems for depth two extensions.