Corrigendum to Cleft Extensions of Hopf Algebroids

Abstract

Theorem 2.2 stated a monoidal isomorphism between the comodule categories of two bialgebroids in a Hopf algebroid. The proof of Theorem 2.2 was based on the journal version of Brzeziński (Ann Univ Ferrara Sez VII (NS) 51:15-27, 2005, Theorem 2.6), whose proof turned out to contain an unjustified step. Here we show that all other results in our paper remain valid if we drop unverified Theorem 2.2, and return to an earlier definition of a comodule of a Hopf algebroid that distinguishes between comodules of the two constituent bialgebroids. Keywords Hopf algebroids · Comodules · Cleft extensions Mathematics Subject Classifications (2000) 16W30 · 58B34 · 16E40 · 19D55Throughout, H is a Hopf algebroid over base algebras L and R (over a commutative ring k), with structure maps denoted as in Section 2.2.Although we are not aware of any counterexamples, the unjustified step found in the proof of the journal version of [7, Theorem 2.6] forces us to reformulate our paper without referring to [7, Theorem 2.6] and our derived Theorem 2.2. In this way we correct also the Examples 2.5(2) and 3.11 in [5], where cleft extensions by HopfThe online version of the original article can be found at http://dx

Corrigendum to “A Schneider type theorem for Hopf algebroids” [J. Algebra 318 (1) (2007) 225–269]

“…The correspondence between such coring extensions and coring maps holds only in a more restricted situation, see [BB3,Corrigendum]. Therefore the beginning of the last paragraph on page 238 should be modified as follows.…”

“…a proper notion of a comodule of a Hopf algebroid, that may differ in general from a comodule of either constituent bialgebroid, the most important results in our paper can be formulated and proven without referring to the objected statements in [Brz3] and [BB2].…”