2009/12/01 by Dorota Marciniak, Marciniak, Dorota, Marcin Szamotulski +1
Mathematics · #06A15 #16T15 #16W30 #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.QA #msc:06A15 #msc:16T15 #msc:16W30
paper · pdf · doi:10.48550/arxiv.0912.0291
Section 5 removed. Shorter lattice theoretic introduction. Same main results. Some statements are stated more clearly
openalex publication_date 2009/12/01 · arxiv created 2011/06/05 · arxiv updated 2011/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce Galois Theory for Hopf-Galois Extensions proving existence of a Galois connection between subalgebras of an H-comodule algebra and generalised quotients of the Hopf algebra H. Moreover, we show that these quotients Q which define Q-Galois extension are the closed elements of our Galois connection. We generalise important results of Hopf--Galois Theory of M. Masuoka and H.-J. Schneider by showing that there is a bijective correspondence between right ideals coideals and right coideal subalgebras of any finite dimensional Hopf algebra and we reformulate the still open problem in the general (i.e. infinite dimensional) case. For cleft extensions we characterise closed elements of the Galois connection as Hopf-Galois extensions. We describe the relation of our results to the work of F. van Oystaeyen, Y. Zhang and also to the results of P. Schauenburg on biGalois extensions.