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首页> 外文期刊>Journal of neurosurgical sciences >COMPUTATION OF HOPE GALOIS STRUCTURES ON LOW DEGREE SEPARABLE EXTENSIONS AND CLASSIFICATION OF THOSE FOR DEGREES p(2) AND 2p
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COMPUTATION OF HOPE GALOIS STRUCTURES ON LOW DEGREE SEPARABLE EXTENSIONS AND CLASSIFICATION OF THOSE FOR DEGREES p(2) AND 2p

机译：计算高度可分离扩展和测量值（2）和2P的低度可分离扩展和分类的希望Galois结构

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摘要

A Hopf Galois structure on a finite field extension L/K is a pair (H, mu), where H is a finite cocommutative K-Hopf algebra and mu a Hopf action. In this paper we present a program written in the computational algebra system Magma which gives all Hopf Galois structures on separable field extensions of degree up to eleven and several properties of those. Besides, we exhibit several results on Hopf Galois structures inspired by the program output. We prove that if (H, mu) is an almost classically Hopf Galois structure, then it is the unique Hopf Galois structure with underlying Hopf algebra H up to isomorphism. For p an odd prime, we prove that a separable extension of degree p(2) may have only one type of Hopf Galois structure and determine those of cyclic type; we determine as well the Hopf Galois structures on separable extensions of degree 2p. We highlight the richness of the results obtained for extensions of degree 8 by computing an explicit example and presenting some tables which summarize these results.
机译：有限局部延伸的HOPF Galois结构L / K是一对（H，MU），其中H是有限的Cocumutative K-Hopf代数和MU A HOPF作用。在本文中，我们展示了一种在计算代数系统岩浆中写入的程序，其赋予所有Hopf Galois结构，其可分离的现场延伸程度高达11个和几种性质。此外，我们对由计划输出的启发的Hopf Galois结构表现出几种结果。我们证明，如果（h，mu）是一个几乎经典的Hopf Galois结构，那么它是独特的Hopf Galois结构，具有底层Hopf代数H蓬松同义。对于P一个奇数的素数，我们证明了程度P（2）的可分离延伸可以只有一种类型的Hopf Galois结构，并确定循环型;我们在2P的可分离延伸方面确定Hopf Galois结构。我们通过计算明确的示例并呈现总结这些结果的一些表来突出所获得的度量8的扩展结果的丰富性。

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