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The decline of Cayley’s invariant theory (1863-1895). (English) Zbl 0662.01010

Im Anschluß an einen früheren Aufsatz des Autors [The rise of Cayley’s invariant theory (1841-1862), ibid. 14, 241-254 (1987; Zbl 0631.01016)] werden hier die von Arthur Cayley (1821-1895) zwischen 1863 und 1895 stammenden Beiträge zur Invariantentheorie beschrieben und mit den parallel laufenden deutschen Beiträgen verglichen. Während die deutsche symbolische Methode in theoretischer Hinsicht große Erfolge zeitigte, wird der expliziten Berechnung und der Darstellung der Invarianten durch Cayley’s Methodik ergänzende Bedeutung zugemessen. Der von Paul Gordan (1868) stammende Hauptsatz der Invariantentheorie (Endlichkeitssatz) wird den von Cayley gefundenen Sätzen vergleichend gegenüber gestellt. Der historische Hintergrund der Cayleyschen Ergebnisse wird an Hand der Korrespondenz mit seinem Freund J. J. Sylvester ausführlich erläutert.
Reviewer: K.Strubecker

MSC:

01A55 History of mathematics in the 19th century

Biographic References:

Cayley, A.

Citations:

Zbl 0631.01016
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References:

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