Braided bi-Galois theory II : The cocommutative case

Schauenburg, Peter

Braided bi-Galois theory II : The cocommutative case

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Datum

2010

Publikationstyp

Zeitschriftenartikel

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Journal of Algebra. 2010, 324(11), pp. 3199-3218. ISSN 0021-8693. Available under: doi: 10.1016/j.jalgebra.2010.07.029

Zusammenfassung

We study groups of bi-Galois objects over a Hopf algebra H in a braided monoidal category Β. We assume H to be cocommutative in a certain sense; this does not mean that H is a cocommutative coalgebra with respect to the braiding given in Β, but it is cocommutative with respect to a different braiding subject to specific axioms. The type of cocommutative Hopf algebras under consideration (investigated in previous papers) occurs naturally, for example in Majid's transmutation construction. We show that for cocommutative H the suitably defined cocommutative bi-Galois objects form a subgroup in the group of H-H-bi-Galois objects. We also show that all cocycles on H are lazy, and that second (lazy) cohomology describes the subgroup of cleft bi-Galois extensions in the group of cocommutative ones.

Fachgebiet (DDC)

510 Mathematik

Schlagwörter

Hopf algebras, Braided categories, Hopf–Galois theory

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ISO 690

SCHAUENBURG, Peter, 2010. Braided bi-Galois theory II : The cocommutative case. In: Journal of Algebra. 2010, 324(11), pp. 3199-3218. ISSN 0021-8693. Available under: doi: 10.1016/j.jalgebra.2010.07.029

BibTex

@article{Schauenburg2010Braid-12759,
  year={2010},
  doi={10.1016/j.jalgebra.2010.07.029},
  title={Braided bi-Galois theory II : The cocommutative case},
  number={11},
  volume={324},
  issn={0021-8693},
  journal={Journal of Algebra},
  pages={3199--3218},
  author={Schauenburg, Peter}
}

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