Writing small omegas : �Elie Cartan's contributions to the theory of continuous groups, 1894-1926 /

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...

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Bibliographic Details
Call Number:Libro Electrónico
Main Author: Cogliati, Alberto (Author)
Format: Electronic eBook
Language:Inglés
Published: London : Academic Press, an imprint of Elsevier, [2018]
Series:Studies in the history of mathematical enquiry.
Subjects:
Continuous groups.
Groupes continus.
MATHEMATICS > Algebra > Intermediate.
Continuous groups
Online Access:Texto completo
Table of Contents:
  • Machine generated contents note: 1. Lie on the Backstage
  • 1.1. Fundamentals of Lie Theory of Finite Continuous Groups
  • 1.1.1. Three Fundamental Theorems
  • 1.1.2. The Adjoint Croup
  • 1.2. "A Fundamental Discipline"
  • 2. Cartan's Doctoral Dissertation
  • 2.1. Finite Continuous Croups
  • 2.1.1. Reduced Form of a Given Group
  • 2.1.2. Solvability and Semisimplicity Criteria
  • 2.1.3. Radical and Decomposition Theorems
  • 2.2. Lie Theory of Complete Systems
  • 2.3. Complete Systems and Canonical Reduction
  • 2.4. Appendix
  • 3. Infinite Continuous Groups 1883
  • 1902
  • 3.1. Lie's First Contributions
  • 3.2. Differential Invariants
  • 3.3. Engel's Habilitationsschrift
  • 3.4. Foundations of Infinite Continuous Groups
  • 3.5. On a Theorem by Engel
  • 3.6. Medolaghi's Contributions
  • 3.7. Vessiot and His Memoire couronnee
  • 4. Exterior Differential Systems
  • 4.1. Some Technical Preliminaries
  • 4.2. The State-of-the-Art in the Early 1890s
  • 4.3. Engel's Invariants Theory of Pfaffian Systems
  • 4.3.1. Invariant Correspondences
  • 4.4. Von Weber's Contributions: 1898
  • 1900
  • 4.4.1. Character and Characteristic Transformations
  • 4.4.2. Pfaffian Systems of Character One
  • 4.4.3. Reducibility of a Pfaffian System to Its Normal Form
  • 4.5. The Foundations of the Exterior Differential Calculus
  • 4.6. Cartan's Theory of General Pfaffian Systems
  • 4.6.1. Geometrical Representation
  • 4.6.2. Cauchy's First Theorem
  • 4.6.3. Genre and Characters
  • 4.6.4. Characteristic Elements
  • 4.6.5. Pfaffian Systems of Character One, II
  • 4.7. Some Final Remarks
  • 5. Cartan's Theory 1902
  • 1909
  • 5.1. On the Genesis of the Theory
  • 5.2. Some Examples
  • 5.3. Cartan's Theory
  • 5.3.1. First Fundamental Theorem
  • 5.3.2. Second and Third Fundamental Theorems
  • 5.4. Subgroups of a Given Continuous Group
  • 5.5. Simple Infinite Continuous Groups
  • 5.6. Essential and Inessential Invariants
  • 5.7. Some Final Remarks
  • 6. Cartan as a Geometer
  • 6.1. Introduction
  • 6.2. Maurer
  • (Cotton)
  • Cartan Forms
  • 6.3. Cartan's 1910 Paper
  • 6.4. The Generalization of the Notion of Space
  • 6.5. Cartan's Collaboration with Schouten
  • 6.6. Concluding Remarks
  • A. Picard
  • Vessiot Theory
  • B. The Galois of His Generation
  • C. Clifford's Parallelism
  • C.1. Klein's Zur Nicht-Euklidischen Geometrie
  • C.2. Bianchi and Fubini
  • C.3. Enea Bortolotti.

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