Twistings, Crossed Coproducts, and Hopf-galois Coextensions
نویسنده
چکیده
Let H be a Hopf algebra. Ju and Cai introduced the notion of twisting of an H-module coalgebra. In this note, we study the relationship between twistings, crossed coproducts and Hopf-Galois coextensions. In particular, we show that a twisting of an H-Galois coextension remains H-Galois if the twisting is invertible.
منابع مشابه
Fixed-point Free Endomorphisms and Hopf Galois Structures
Let L|K be a Galois extension of fields with finite Galois group G. Greither and Pareigis [GP87] showed that there is a bijection between Hopf Galois structures on L|K and regular subgroups of Perm(G) normalized by G, and Byott [By96] translated the problem into that of finding equivalence classes of embeddings of G in the holomorph of groups N of the same cardinality as G. In [CCo06] we showed...
متن کاملKrull relations in Hopf Galois extensions: Lifting and twisting
This paper continues our study, begun in [MS], of the relationship between the prime ideals of an algebra A and of a subalgebra R such that R ⊂A is a faithfully flat H -Galois extension, for some finite-dimensional Hopf algebra H . In that paper we defined three basic Krull relations, Incomparability (INC), t-Lying Over (t-LO), and Going Up (GU), analogous to the classical Krull relations for p...
متن کاملSome Topics On Braided Hopf Algebras And Galois Extension in Braided Tensor Categories
Braided Hopf algebras have attracted much attention in both mathematics and mathematical physics (see e.g. [2][4][14][16][17][18][20][23]). The classification of finite dimensional Hopf algebras is interesting and important for their applications (see [1] [24]). Braided Hopf algebras play an important role in the classification of finite-dimensional pointed Hopf algebras (e.g. [1][2] [21]). The...
متن کاملOn Algebraic Construction in Braided Tensor Categories
Braided Hopf algebras have attracted much attention in both mathematics and mathematical physics (see e.g. [1][4][13][15][17][16][20][23]). The classification of finite dimensional Hopf algebras is interesting and important for their applications (see [2] [22]). Braided Hopf algebras play an important role in the classification of finite-dimensional pointed Hopf algebras (e.g. [2][1] [19]). The...
متن کاملPseudo-galois Extensions and Hopf Algebroids
Pseudo-Galois extensions are shown to be depth two extensions. Studying its left bialgebroid, we construct an enveloping Hopf algebroid for the semi-direct product of groups or involutive Hopf algebras and their module algebras. It is a type of cofibered sum of two inclusions of the Hopf algebra into the semi-direct product and its derived right crossed product. Van Oystaeyen and Panaite observ...
متن کامل