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The metabolicity index of involutions in characteristic two
Journal of Pure and Applied Algebra ( IF 0.7 ) Pub Date : 2021-02-12 , DOI: 10.1016/j.jpaa.2021.106716
A.-H. Nokhodkar

We define the notion of metabolicity index of involutions of the first kind in characteristic two. It is shown that this index is preserved over odd degree extensions of the base field. Also, its behavior over finite separable extensions is studied. As an application, it is shown that an orthogonal involution on a central simple algebra of degree a power of two which is either anisotropic or metabolic is totally decomposable if it is totally decomposable over some separable extension of the ground field. This result is then used to strengthen an earlier result of the author which proves a characteristic two counterpart of a conjecture concerning Pfister involutions formulated by Bayer-Fluckiger et al.



中文翻译:

特征二的对合代谢指数

我们在特征二中定义了第一类对合代谢指数的概念。结果表明,该索引保留在基础字段的奇数阶扩展上。此外,还研究了它在有限可分离扩展上的行为。作为一个应用,证明了如果它在地面场的一些可分离扩展上是完全可分解的,那么在各向异性为2或幂的二次方的中心简单代数上的正交对合是完全可分解的。然后,该结果被用于加强作者的早期结果,该结果证明了由Bayer-Fluckiger等人提出的关于Pfister对合的猜想的特征性的两个对应物。

更新日期:2021-02-18
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