Cover of: Emergence of the Theory of Lie Groups by Hawkins, Thomas

Emergence of the Theory of Lie Groups

An Essay in the History of Mathematics 1869-1926

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Last edited by MARC Bot
June 30, 2019 | History

Emergence of the Theory of Lie Groups

An Essay in the History of Mathematics 1869-1926

  • 0 Ratings
  • 0 Want to read
  • 0 Currently reading
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Publish Date
Publisher
Springer New York
Language
English
Pages
566

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Written by the recipient of the 1997 MAA Chauvenet Prize for mathematical exposition, this book tells how the theory of Lie groups emerged from a fascinating cross fertilization of many strains of 19th and early 20th century geometry, analysis, mathematical physics, algebra and topology. The reader will meet a host of mathematicians from the period and become acquainted with the major mathematical schools. The first part describes the geometrical and analytical considerations that initiated the theory at the hands of the Norwegian mathematician, Sophus Lie. The main figure in the second part is Weierstrass'student Wilhelm Killing, whose interest in the foundations of non-Euclidean geometry led to his discovery of almost all the central concepts and theorems on the structure and classification of semisimple Lie algebras. The scene then shifts to the Paris mathematical community and Elie Cartans work on the representation of Lie algebras. The final part describes the influential, unifying contributions of Hermann Weyl and their context: Hilberts Göttingen, general relativity and the Frobenius-Schur theory of characters. The book is written with the conviction that mathematical understanding is deepened by familiarity with underlying motivations and the less formal, more intuitive manner of original conception. The human side of the story is evoked through extensive use of correspondence between mathematicians. The book should prove enlightening to a broad range of readers, including prospective students of Lie theory, mathematicians, physicists and historians and philosophers of science.

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Edition Availability
Cover of: Emergence of the Theory of Lie Groups
Cover of: Emergence of the Theory of Lie Groups
Emergence of the Theory of Lie Groups: An Essay in the History of Mathematics 1869-1926
2000, Springer New York
electronic resource : in English

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Book Details


Published in

New York, NY

Table of Contents

Preface
The Geometrical Origins of Lie's theory
Jacobi & The Analytical Origins of Lie's Theory
Lie's Theory of Transformation Groups 1874-1893
Non-euclidean Geometry & Weierstrassian Mathematics
Killing & the Structure of Lie Algebras
The Doctoral Thesis of Elie Cartan
Lie's School & Linear Representations
Cartan's Trilogy: 1913-14
The Göttingen School of Hilbert
The Berlin Algebraists: Frobenius & Schur
From Relativity to Representations
Weyl's Great Papers of 1925 & 1926
References
Index.

Edition Notes

Online full text is restricted to subscribers.

Also available in print.

Mode of access: World Wide Web.

Series
Sources and Studies in the History of Mathematics and Physical Sciences, Sources and studies in the history of mathematics and physical sciences

Classifications

Dewey Decimal Class
512.2
Library of Congress
QA174-183

The Physical Object

Format
[electronic resource] :
Pagination
1 online resource (xiii, 566 p.)
Number of pages
566

ID Numbers

Open Library
OL27035856M
ISBN 10
1461270421, 1461212022
ISBN 13
9781461270423, 9781461212027
OCLC/WorldCat
853269676

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