2007/01/02 by Gabriella Böhm, Böhm, Gabriella
Mathematics · #16W30 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #math.QA #math.RA #msc:16W30
paper · pdf · doi:10.48550/arxiv.math/0701064
written form of a talk, LaTeX file, 27 pages. v2: Substantial revision, distinguishing between comodules of both constituent bialgebroids in a Hopf algebroid
openalex publication_date 2007/01/02 · arxiv created 2008/11/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/03
This paper is a written form of a talk. It gives a review of various notions of Galois (and in particular cleft) extensions. Extensions by coalgebras,bialgebras and Hopf algebras (over a commutative base ring) and by corings,bialgebroids and Hopf algebroids (over a non-commutative base algebra) are systematically recalled and compared. In the first version of this paper, the journal version of [15, Theorem 2.6] was heavily used, in two respects. First, it was applied to establish an isomorphism between the comodule categories of two constituent bialgebroids in a Hopf algebroid. Second, it was used to construct a Morita context for any bicomodule for a coring extension. Regrettably, it turned out that the proof of [15, Theorem 2.6] contains an unjustified step. Therefore, our derived results are not expected to hold at the stated level of generality either. In the revised version we make the necessary corrections in both respects. In doing so, we obtain a corrected version of \cite[5, Theorem 4.2] as well, whose original proof contains a very similar error to [15, Theorem 2.6].