Writing Small Omegas

Elie Cartan's Contributions to the Theory of Continuous Groups 1894-1926
Erscheinungsjahr 2017
ISBN: 978-0-12-814244-8
Verlag: Elsevier Science Publishing Co Inc

Buch, Englisch, 304 Seiten, Format (B × H): 230 mm x 152 mm, Gewicht: 504 g

Writing Small Omegas: Elie Cartan's Contributions to the Theory of Continuous Groups 1894-1926 provides a general account of Lie's theory of finite continuous groups, critically examining Cartan's doctoral attempts to rigorously classify simple Lie algebras, including the use of many unpublished letters. It evaluates pioneering attempts to generalize Lie's classical ideas to the infinite-dimensional case in the works of Lie, Engel, Medolaghi and Vessiot. Within this context, Cartan's groundbreaking contributions in continuous group theory, particularly in his characteristic and unique recourse to exterior differential calculus, are introduced and discussed at length.

The work concludes by discussing Cartan's contributions to the structural theory of infinite continuous groups, his method of moving frames, and the genesis of his geometrical theory of Lie groups.

Zielgruppe

<p>1<SUP>st</SUP> year PhD students, advanced graduate students and tenured mathematicians and historians of mathematics with an interest in differential geometry, Lie algebras and continuous groups.</p>

Autoren/Hrsg.

Cogliati, Alberto

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Geschichte der Naturwissenschaften, Formalen Wissenschaften & Technik
• Mathematik | Informatik Mathematik Mathematik Allgemein Geschichte der Mathematik
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie

Inhaltsverzeichnis

1. Lie on the backstage2. Cartan's doctoral dissertation3. Infinite Continuous Groups 1883-19024. Exterior Differential Systems5. Cartan's Theory (1902-1909)6. The method of moving frames7. The geometry of continuous groups8. Conclusion

Über Autor(innen)

Cogliati, Alberto
Alberto Cogliati, currently Assistant Professor at the Department of Mathematics 'F. Enriques' of the Università degli Studi di Milano. He received his PhD in March 2012 discussing Cartan's structural approach to the theory of continuous groups of transformations. His main research interest is the history of 19th-20th mathematics, especially differential geometry, the history of Lie groups and the theory of connections.