群$$s_6$$和$$A_7的Felix Klein投影表示$$

IF 0.7 2区哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE

Archive for History of Exact Sciences Pub Date : 2022-04-25 DOI:10.1007/s00407-022-00290-x

Henning Heller

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引用次数: 2

摘要

本文介绍了费利克斯·克莱因在1886年的一篇文章，他在文章中将他的5次多项式方程理论推广到6次和7次方程，这一理论在两年前的二十面体讲座中进行了全面讨论。为此，Klein使用了先前在线几何中建立的结果。我回顾了克莱因1886年的文章，它多样化的数学背景，以及它在更广泛的数学史中的地位。我认为，这篇文章提出的程序，尽管由于其最终的失败而在历史上被忽视，但它提供了对该主题关键演变时期的宝贵见解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

$Felix Klein’s projective representations of the groups $S_6$ and $A_7$$

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Felix Klein’s projective representations of the groups $S_6$ and $A_7$

This paper addresses an article by Felix Klein of 1886, in which he generalized his theory of polynomial equations of degree 5—comprehensively discussed in his Lectures on the Icosahedron two years earlier—to equations of degree 6 and 7. To do so, Klein used results previously established in line geometry. I review Klein’s 1886 article, its diverse mathematical background, and its place within the broader history of mathematics. I argue that the program advanced by this article, although historically overlooked due to its eventual failure, offers a valuable insight into a time of crucial evolution of the subject.

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来源期刊

Archive for History of Exact Sciences 管理科学-科学史与科学哲学

CiteScore

1.30

自引率

20.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Archive for History of Exact Sciences casts light upon the conceptual groundwork of the sciences by analyzing the historical course of rigorous quantitative thought and the precise theory of nature in the fields of mathematics, physics, technical chemistry, computer science, astronomy, and the biological sciences, embracing as well their connections to experiment. This journal nourishes historical research meeting the standards of the mathematical sciences. Its aim is to give rapid and full publication to writings of exceptional depth, scope, and permanence.