2005/02/09 by Lars Kadison, Kadison, Lars · 1 citation
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/0502188
19 pp., to appear in Proceedings of the "Ferrara Algebra Workshop" jointly with the "Workshop on Hopf Algebras,Swansea" (to be published as a special issue of the "Annali dell'Universita' di Ferrara, sez. VII, Scienze Matematiche)
arxiv created 2005/02/09 · arxiv updated 2009/12/01
We reduce certain proofs in math.RA/0108067, math.RA/0408155, and math.QA/0409589 to depth two quasibases from one side only, a minimalistic approach which leads to a characterization of Galois extensions for finite projective bialgebroids without the Frobenius extension property. We prove that a proper algebra extension is a left T-Galois extension for some right finite projective left bialgebroid over some algebra R if and only if it is a left depth two and left balanced extension. Exchanging left and right in this statement, we have a characterization of right Galois extensions for left finite projective right bialgebroids. Looking to examples of depth two, we establish that a Hopf subalgebra is normal if and only if it is a Hopf-Galois extension. We characterize finite weak Hopf-Galois extensions using an alternate Galois canonical mapping with several corollaries: that these are depth two and that surjectivity of the Galois mapping implies its bijectivity.