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Hopf Galois structures on separable field extensions of odd prime power degree

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1 Published in 2019 at "Journal of Algebra"

DOI: 10.1016/j.jalgebra.2018.11.004

Abstract: A Hopf Galois structure on a finite field extension $L/K$ is a pair $(\mathcal{H},\mu)$, where $\mathcal{H}$ is a finite cocommutative $K$-Hopf algebra and $\mu$ a Hopf action. In this paper, we present several results on… read more here.

Keywords: field; extension; galois structures; hopf galois ... See more keywords

Hopf Galois structures on field extensions of degree twice an odd prime square and their associated skew left braces

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1 Published in 2020 at "Journal of Algebra"

DOI: 10.1016/j.jalgebra.2020.09.005

Abstract: Abstract We determine the Hopf Galois structures on a Galois field extension of degree twice an odd prime square and classify the corresponding skew left braces. Besides we determine the separable field extensions of degree… read more here.

Keywords: degree twice; twice odd; field; odd prime ... See more keywords

Hopf-Galois structures on finite extensions with almost simple Galois group

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1 Published in 2020 at "Journal of Number Theory"

DOI: 10.1016/j.jnt.2020.04.003

Abstract: Abstract In this paper, we study the Hopf-Galois structures on a finite Galois extension whose Galois group G is an almost simple group in which the socle A has prime index p. Each Hopf-Galois structure… read more here.

Keywords: almost simple; group; galois group; hopf galois ... See more keywords

Morita equivalence for weak Hopf–Galois extensions

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0 Published in 2017 at "Communications in Algebra"

DOI: 10.1080/00927872.2016.1175572

Abstract: ABSTRACT Let H be a commutative weak Hopf algebra over a fixed field k, and A,B be weak H-Hopf Galois extensions. In this paper, we give a structure theorem for the category of weak relative… read more here.

Keywords: hopf; galois extensions; hopf galois; weak hopf ... See more keywords

Normality and short exact sequences of Hopf-Galois structures

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0 Published in 2019 at "Communications in Algebra"

DOI: 10.1080/00927872.2018.1529237

Abstract: Abstract Every Hopf-Galois structure on a finite Galois extension K/k where corresponds uniquely to a regular subgroup , normalized by , in accordance with a theorem of Greither and Pareigis. The resulting Hopf algebra which… read more here.

Keywords: short exact; galois structure; hopf galois; exact sequences ... See more keywords

Gorenstein Flat Modules of Hopf-Galois Extensions

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1 Published in 2023 at "Mathematics"

DOI: 10.3390/math11112542

Abstract: Let A/B be a right H-Galois extension over a semisimple Hopf algebra H. The purpose of this paper is to give the relationship of Gorenstein flat dimensions between the algebra A and its subalgebra B,… read more here.

Keywords: flat modules; hopf galois; gorenstein flat; modules hopf ... See more keywords