Emergence of the Theory of Lie Groups

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, ...

Emergence of the Theory of Lie Groups

The great Norwegian mathematician Sophus Lie developed the general theory of transformations in the 1870s, and the first part of the book properly focuses on his work. In the second part the central figure is Wilhelm Killing, who developed structure and classification of semisimple Lie algebras. The third part focuses on the developments of the representation of Lie algebras, in particular the work of Elie Cartan. The book concludes with the work of Hermann Weyl and his contemporaries on the structure and representation of Lie groups which serves to bring together much of the earlier work into a coherent theory while at the same time opening up significant avenues for further work.

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Emergence of the Theory of Lie Groups
Language: en
Pages: 566
Authors: Thomas Hawkins
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

The great Norwegian mathematician Sophus Lie developed the general theory of transformations in the 1870s, and the first part of the book properly focuses on his work. In the second part the central figure is Wilhelm Killing, who developed structure and classification of semisimple Lie algebras. The third part focuses
Structure and Geometry of Lie Groups
Language: en
Pages: 746
Authors: Joachim Hilgert, Karl-Hermann Neeb
Categories: Mathematics
Type: BOOK - Published: 2011-11-06 - Publisher: Springer Science & Business Media

This self-contained text is an excellent introduction to Lie groups and their actions on manifolds. The authors start with an elementary discussion of matrix groups, followed by chapters devoted to the basic structure and representation theory of finite dimensinal Lie algebras. They then turn to global issues, demonstrating the key
Essays in the History of Lie Groups and Algebraic Groups
Language: en
Pages: 184
Authors: Armand Borel
Categories: Mathematics
Type: BOOK - Published: 2001 - Publisher: American Mathematical Soc.

This book looks at the development of lie groups and algebraic groups, highlighting the evolution from the almost purely local theory at the start to the global theory that we know today. Starting from Lie's theory of local analytic transformation groups and early work on Lie algebras, he follows the
Fundamentals of Advanced Mathematics V3
Language: en
Pages: 424
Authors: Henri Bourles
Categories: Mathematics
Type: BOOK - Published: 2019-10-11 - Publisher: Elsevier

Fundamentals of Advanced Mathematics, Volume Three, begins with the study of differential and analytic infinite-dimensional manifolds, then progresses into fibered bundles, in particular, tangent and cotangent bundles. In addition, subjects covered include the tensor calculus on manifolds, differential and integral calculus on manifolds (general Stokes formula, integral curves and manifolds),
Emergence of the Theory of Lie Groups
Language: en
Pages: 584
Authors: Thomas Hawkins
Categories: Mathematics
Type: BOOK - Published: 2000-07-19 - Publisher:

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