BOOKS
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Textbooks:
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Other Books on Lie Groups/Lie Algebras:
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William Fulton and Joe Harris,
Representation Theory: A First Course,
Springer-Verlag, 1991.
An excellent graduate mathematics text.
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Karin Erdmann and Mark J. Wildon,
Introduction to Lie Algebras,
Springer Verlag, 2006
Suitable for advanced undergraduates;
a somewhat easier read than Fulton & Harris.
Online access is available through the OSU library.
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William M. Boothby,
An Introduction to Differential Manifolds and Riemannian Geometry,
Academic Press, 1975 (2nd edition: 1986; revised 2nd edition: 2002)
A graduate-level introduction to differential geometry;
discusses Lie groups and Lie algebras.
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Anthony Zee,
Group Theory in a Nutshell for Physicists,
Princeton University Press, 2016
All of the essential math is here, with lots of details and applications to
physics.