Hesse's principle of transfer
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In geometry, Hesse's principle of transfer (German: Übertragungsprinzip) states that if the points of the projective line P1 are depicted by a rational normal curve in Pn, then the group of the projective transformations of Pn that preserve the curve is isomorphic to the group of the projective transformations of P1 (this is a generalization of the original Hesse's principle, in a form suggested by Wilhelm Franz Meyer).[1][2] It was originally introduced by Otto Hesse in 1866, in a more restricted form. It influenced Felix Klein in the development of the Erlangen program.[3][4][5] Since its original conception, it was generalized by many mathematicians, including Klein, Fano, and Cartan.[6]
See also
Further reading
- Hawkins, Thomas (1988). "Hesses's principle of transfer and the representation of lie algebras", Archive for History of Exact Sciences, 39(1), pp. 41–73.
References
- ↑ W.F. Meyer. Apolaritat Und Rationale Curven. ISBN 978-5-87713-744-8. https://books.google.com/books?id=t-wOAwAAQBAJ.
- ↑ Akivis, M. A.; Rosenfeld, B. A. (2011) (in en). Élie Cartan (1869–1951). American Mathematical Soc.. pp. 102, 107–108. ISBN 9780821853559. https://books.google.com/books?id=_8eaAwAAQBAJ&pg=PA102.
- ↑ Kolmogorov, Andrei N., ed (2012) (in en). Mathematics of the 19th Century: Geometry, Analytic Function Theory. Birkhäuser. p. 111. ISBN 9783034891738. https://books.google.com/books?id=XTYDCAAAQBAJ&pg=PA111.
- ↑ Marquis, Jean-Pierre (2008) (in en). From a Geometrical Point of View: A Study of the History and Philosophy of Category Theory. Springer Science & Business Media. p. 25. ISBN 9781402093845. https://books.google.com/books?id=bvy0aANuhPYC&pg=PA25.
- ↑ Richter-Gebert, Jürgen (2011) (in en). Perspectives on Projective Geometry: A Guided Tour Through Real and Complex Geometry. Springer Science & Business Media. p. 179. ISBN 9783642172861. https://books.google.com/books?id=F_NP8Kub2XYC&pg=PA179.
- ↑ Hawkins, Thomas (2000) (in en). Emergence of the Theory of Lie Groups: An Essay in the History of Mathematics 1869–1926. Springer Science & Business Media. pp. 234 and 294. ISBN 9780387989631. https://archive.org/details/emergenceoftheor0000hawk.
Original reference
- Hesse, L. O. (1866). "Ein Uebertragungsprinzip", Crelle's Journal.
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