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eBook Lie Groups, Lie Algebras, and Representations: An Elementary Introduction epub

by Brian Hall

eBook Lie Groups, Lie Algebras, and Representations: An Elementary Introduction epub
  • ISBN: 0387401229
  • Author: Brian Hall
  • Genre: Science
  • Subcategory: Mathematics
  • Language: English
  • Publisher: Springer; 1st ed. 2003. Corr. 2nd printing 2004 edition (August 27, 2004)
  • Pages: 354 pages
  • ePUB size: 1370 kb
  • FB2 size 1646 kb
  • Formats rtf azw mbr lit


This book addresses Lie groups, Lie algebras, and representation theory. The first covers Lie groups and Lie algebras and the relationship between them, along with basic representation theory.

This book addresses Lie groups, Lie algebras, and representation theory. The second part covers the theory of semisimple Lie groups and Lie algebras, beginning with a detailed analysis of the representations of SU(3). The author illustrates the general theory with numerous images pertaining to Lie algebras of rank two and rank three, including images of root systems, lattices of dominant integral weights, and weight diagrams.

This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites

This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. Covers the core topics of Lie theory from an elementary point of view. Includes many new exercises.

Abstract: These notes give an elementary introduction to Lie groups, Lie algebras, and their representations. Topics include definitions and examples of Lie groups and Lie algebras, the relationship between Lie groups and Lie algebras via the exponential mapping, the basics of representations theory, the orff formula, a detailed study of the representations of SU(3), and a brief survey of the representation theory of general semisimple groups.

This textbook treats Lie groups, Lie algebras and their representations in an elem. An Introduction to Lie Groups and Lie Algebras. ALEXANDER KIRILLOV, Jr. Lie Groups, Lie Algebras, and Representations: An Elementary Introduction. 27 MB·17 Downloads·New! introduction to the machinery of semi simple groups and Lie algebras by treating the rep. Kirillov A. An Introduction to Lie Groups and Lie Algebras Lie Groups, Lie Algebras, And Representations An Elementary Introduction. 07 MB·2 Downloads·New!. Spy the Lie: Former CIA Officers Teach You How to Detect Deception.

This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion .

This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the subject.

This book provides an introduction to Lie groups, Lie algebras, and repre­ sentation theory, aimed at graduate .

This book provides an introduction to Lie groups, Lie algebras, and repre­ sentation theory, aimed at graduate students in mathematics and physics. Although there are already several excellent books that cover many of the same topics, this book has two distinctive features that I hope will make it a useful addition to the literature. Second, this book provides a gentle introduction to the machinery of semi simple groups and Lie algebras by treating the representation theory of SU(2) and SU(3) in detail before going to the general case. This allows the reader to see roots, weights, and the Weyl group "in action" in simple cases before confronting the general theory.

The first covers Lie groups and Lie algebras and the relationship between them, along with basic representation theory. Brian Hall is an Associate Professor of Mathematics at the University of Notre Dame.

This book provides an introduction to Lie groups, Lie algebras, and repre sentation theory, aimed at graduate students in mathematics and physics

This book provides an introduction to Lie groups, Lie algebras, and repre sentation theory, aimed at graduate students in mathematics and physics. This book provides an introduction to Lie groups, Lie algebras, and repre sentation theory, aimed at graduate students in mathematics and physics.

Lie groups, Lie algebras, and representation theory are the main focus of this text. In order to keep the prerequisites to a minimum, the author restricts attention to matrix Lie groups and Lie algebras. This approach keeps the discussion concrete, allows the reader to get to the heart of the subject quickly, and covers all of the most interesting examples. The book also introduces the often-intimidating machinery of roots and the Weyl group in a gradual way, using examples and representation theory as motivation. The text is divided into two parts. The first covers Lie groups and Lie algebras and the relationship between them, along with basic representation theory. The second part covers the theory of semisimple Lie groups and Lie algebras, beginning with a detailed analysis of the representations of SU(3). The author illustrates the general theory with numerous images pertaining to Lie algebras of rank two and rank three, including images of root systems, lattices of dominant integral weights, and weight diagrams. This book is sure to become a standard textbook for graduate students in mathematics and physics with little or no prior exposure to Lie theory. Brian Hall is an Associate Professor of Mathematics at the University of Notre Dame.

Comments: (7)
Prorahun
Brian Hall has written the best book I know (and I have several) on this challenging topic. The concepts are easy, but the number of different kinds of things one needs to remember to master this topic, to apply it, and to do calculations with it is large. Hall takes the time to spell out the structure and relationships that make remembering the "zoo" much easier, at least for me. If you're inclined to remember things by their structure and relationships (as opposed to their mere taxonomy), then you will get a lot out of this book.
Falya
This book is very well introduction to this topic because have a minimal prerequisites. For example Part 1 using only Linear algebra. Furthermore, in Part 1 Hall explains matrix Lie groups with many examples and some geometrical-physical interpretations. I recommend this book for both mathematicians and physicists.
Katishi
I used this text last year for a third year undergraduate course on Lie groups, Lie algebras and representations and it was excellent! I found the exposition to be super clear and easy to follow. Also, I really loved an entire chapter that focused on the representation theory of $mathfrak{sl}_3(Bbb{C})$! As I grow older, I discover more and more the importance of having a concrete grasp of examples - and Brian's book does it in exactly that way. Plus, it is not disorganized and does not handwave like Fulton and Harris (which has gaps in its proofs using Weight diagrams in the chapter on representations of $mathfrak{sl}_3$) and is not dry and abstract like Humphreys' book!

I would say that this is the best book out there to start learning Lie theory from.
Ylonean
Great book and service!
Jesmi
I love this book. I like to think I am a good mathematician, but I have always had a lot of trouble with differential geometry. I suspect there are a lot of people out there like me. This book presents Lie Groups using matrix groups, which makes things much more concrete. The book is not easy, and requires good linear algebra skills. However, many matrix algebra theorems are presented and proved in the appendices. The appendices also include the abstract definitions of Lie groups and algebras for general manifolds which are topological groups, with examples, and the author always explains how the theorems for matrix groups relate to those for general Lie groups, and in many cases little modification seems to be necessary.

There are plenty of exercises at the end of each chapter that are of just the right difficulty to help you understand the material.

I got the first edition, since the second edition seems to be available only in paperback and I prefer hardcover. There seem to be a lot of typos in the first edition that are easy to spot. I imagine they have been corrected in the second edition. I don't know what other changes were made.

Some people who reviewed this book complained that it does not fully reveal the pristine beauty of general Lie groups. This may be true, but a book that I cannot read is not going to do me any good. Also, many people who use Lie Groups only really need matrix groups and this may be a good book for them.
Kulalbine
[EDITED 2012: This review used to contain information about the (unreadable) Kindle edition of this book. I removed that information after the publisher, wisely, stopped offering the Kindle edition.]

As a graduate student, I love this book. It requires surprisingly little familiarity with topology and algebra; I could have taken this course in my first year without being taxed by prerequisites. Its focus on specific examples, such as SU(2) and SO(3), match well with the situations in which I have previously encountered Lie groups outside of the course. The extensive discussion of examples also helps me to structure the big picture in my head, in that I feel more confident asserting why we take an interest in, for example, the connectedness of a Lie group. Hall's discussion of the behavior of, and topological properties of, the most commonly encountered Lie groups is superb. The writing clarifies which details I ought to work out on my own as I read (which is another reason I would have been able to take this course in my first year, when my skill at actively reading and engaging with upper-level textbooks was still budding).

I don't know if this book is useful as a reference text for individuals who have a research interest in algebraic topology. I doubt it's extensive enough. However, as a learning text for physicists and mathematicians whose main research interest lies in analysis or PDE, this book has proven very satisfactory. Future authors of textbooks might also skim through it to discover an excellent example of how to connect with a competent student audience and guide them into an unfamiliar topic without obscuring its purpose.

Also worth recommending here, specifically as a companion volume: the text Linearity, Symmetry, and Prediction in the Hydrogen Atom (Undergraduate Texts in Mathematics) by Stephanie Frank Singer. I think an excellent and interesting first-year graduate course in mathematical physics could be constructed from Hall's and Singer's books.
Grosho
Great book!
good
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