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Article ID: CBB746243101

Felix Klein’s projective representations of the groups S6 and A7 (2022)

Heller, Henning (Author)

Archive for History of Exact Sciences
Volume: 76
Issue: 5
Pages: 431-470

DOI: 10.1007/s00407-022-00290-x

URI: https://doi.org/10.1007/s00407-022-00290-x

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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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