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Lie Groups: An Introduction Through Linear Groups
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Lie Groups: An Introduction Through Linear Groups Hardcover - 2002 - 1st Edition

by Wulf Rossman


From the publisher

This book is an introduction to the theory of Lie groups and their representations at the advanced undergraduate or beginning graduate level. It covers the essentials of the subject starting from basic undergraduate mathematics. The correspondence between linear Lie groups and Lie algebras is developed in its local and global aspects. The classical groups are analyzed in detail, first with elementary matrix methods, then with the help of the structural tools typical of the theory of semisimple groups, such as Cartan subgroups, root, weights and reflections. The fundamental groups of the classical groups are worked out as an application of these methods. Manifolds are introduced when needed, in connection with homogeneous spaces, and the elements of differential and integral calculus on manifolds are presented, with special emphasis on integration on groups and homogeneous spaces. Representation theory starts from first principles, such as Schur's lemma and its consequences, and
proceeds from there to the Peter-Weyl theorem, Weyl's character formula, and the Borel-Weil theorem, all in the context of linear groups.

First line

A linear transformation X of the n-dimensional real or complex vector space E can be thought of as a vector field: X associates to each point p in E, the vector X(p).

Details

  • Title Lie Groups: An Introduction Through Linear Groups
  • Author Wulf Rossman
  • Binding Hardcover
  • Edition number 1st
  • Edition 1
  • Pages 282
  • Volumes 1
  • Language ENG
  • Publisher OUP Oxford, Oxford
  • Date 2002-03-21
  • Illustrated Yes
  • ISBN 9780198596837 / 0198596839
  • Weight 1.24 lbs (0.56 kg)
  • Dimensions 8.6 x 5.9 x 0.79 in (21.84 x 14.99 x 2.01 cm)
  • Library of Congress subjects Lie groups
  • Library of Congress Catalog Number 2001050008
  • Dewey Decimal Code 512.55
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Lie Groups: An Introduction Through Linear Groups (Oxford Graduate Texts in Mathematics, 5)

Lie Groups: An Introduction Through Linear Groups (Oxford Graduate Texts in Mathematics, 5)

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Lie Groups : An Introduction Through Linear Groups
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Lie Groups: An Introduction through Linear Groups (Oxford Graduate Texts in Mathematics, 5)
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