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Field name	Details
Dewey Class	512.482 (DDC 22)
Title	Lie groups and lie algebras : a physicist's perspective ([Ebook]) / Adam B. Bincer
Author	Bincer, Adam M.
Other name(s)	Oxford Scholarship Online
Publication	Oxford, UK : Oxford University Press , 2013
Physical Details	1 online resource
ISBN	9780191745492
Note	Published in print: 2012. - Published Online: January 2013. - ISBN:9780199662920. - eISBN: 9780191745492
Summary Note	This book is based on lectures given to graduate students in physics at the University of Wisconsin-Madison. Group theory has been around for many years and the only thing new in this book is my approach to the subject, in particular the attempt to emphasize its beauty. The inspiration was this quote from Hermann Weyl: “My work always tried to unite the true with the beautiful; but when I had to choose one or the other I usually chose the beautiful”. The book starts with the definition of basic concepts such as group, vector space, algebra, Lie group, Lie algebra, simple and semisimple groups, compact and non-compact groups. Next SO(3) and SU(2) are introduced as examples of elementary Lie groups and their relation to Physics and angular momentum. All irreducible representations, addition of angular momentum, Clebsch–Gordan coefficients and the Wigner–Eckart theorem are presented. Next the so(n) algebras and spinors are discussed using Clifford numbers. Conjugate, orthogonal and symplectic representations of spinors are described and the Clebsch–Gordan series for spinors is given, followed by a description of the center and outer automorphisms of Spin(n). The book next presents a diversion on Hurwitz’s theorem, quaternions and octonions, which leads into a discussion of the exceptional group G 2. The discussion of orthogonal groups is concluded with a presentation of their Casimir operators. As a lead in to unitary groups the book discusses classical groups and obtain the dimensions of orthogonal, unitary and symplectic groups in one fell swoop by treating them as unitary groups over the reals, the complex and the quaternions, respectively. The symmetric group Sr is introduced and used to discuss irreducible representations of SU(n). The next three chapters involve the Cartan basis, the Cartan classification of semisimple algebras and Dynkin diagrams. The last three chapters are of particular importance to physicists as they describe the space-time groups known as the Lorentz, Poincaré and Liouville groups and the energy levels of the hydrogen atom in n space dimensions. At the end of each chapter brief biographical notes are given on the scientist(s) mentioned in that chapter for the first time.:
Mode of acces to digital resource	Digital reproduction. - Oxford : Oxford University Press, 2013. - Access through World Wide Web. The text is recorded in HTML
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1093/acprof:oso/9780199662920.001.0001
Links to Related Works	Subject References: Group theory . Lie algebras . Lie groups . Authors: Bincer, Adam M. . Corporate Authors: Oxford Scholarship Online . Classification: 512.482 (DDC 22) .

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Lie groups and lie algebras: a physicist's perspective

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