Lie Groups, Lie Algebras, and Representations: An Elementary Introduction (Graduate Texts in Mathematics, 222)

Lie Groups, Lie Algebras, and Representations: An Elementary Introduction (Graduate Texts in Mathematics, 222)

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Lie Groups, Lie Algebras, and Representations: An Elementary Introduction (Graduate Texts in Mathematics, 222)

Lie Groups, Lie Algebras, and Representations: An Elementary Introduction (Graduate Texts in Mathematics, 222)

Written by Brian C. Hall
4.85 70,543 ratings
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About this ebook:
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.In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including:* a treatment of the Baker-Campbell-Hausdorff formula and its use in place of the Frobenius theorem to establish deeper results about the relationship between Lie groups and Lie algebras* motivation for the machinery of roots, weights and the Weyl group via a concrete and detailed exposition of the representation theory of sl(3;C)* rapidly develops the structure of semisimple Lie algebras by using a definition of semisimplicity that is unconventional but equivalent to the standard one* gives independent constructions of the representations of semisimple Lie algebras and compact Lie groupsThe second edition of Lie Groups, Lie Algebras, and Representations contains many substantial improvements and additions, among them: an entirely new part devoted to the structure and representation theory of compact Lie groups; a complete derivation of the main properties of root systems; the construction of finite-dimensional representations of semisimple Lie algebras has been elaborated; a treatment of universal enveloping algebras, including a proof of the Poincare Birkhoff Witt theorem and the existence of Verma modules; complete proofs of the Weyl character formula, the Weyl dimension formula and the Kostant multiplicity formula. The new edition also includes many additional figures.

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Pages 453
Language Eng
Publisher Springer
Published August 7, 2003
ISBN 26496725
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Brian C. Hall
About the Author
Brian C. Hall

After spending years working in the corporate world, Brian C. Hall finally decided to pursue a lifelong passion for writing. They currently reside in a quiet suburb where they spend most of their time outlining new stories, reading extensively, and occasionally attempting to bake.

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Ashley Wilson November 27, 2024
Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
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Linda Sanchez July 26, 2024
A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
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A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
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Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
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Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
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Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
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William Baker
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A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
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Excellent, though slightly flawed. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
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Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. I would highly recommend this to discerning readers.
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David Martinez May 20, 2025
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Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
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A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
Kevin Thomas
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Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
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Excellent, though slightly flawed. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
Joseph Rivera
Joseph Rivera October 13, 2024
A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend.
Eric Gomez
Eric Gomez May 13, 2025
It was adequate. The prose was competent, yet the characters lacked the depth I usually seek. Suitable if your reading queue is empty.
Thomas Clark
Thomas Clark April 29, 2025
A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
Emily Turner
Emily Turner July 04, 2025
Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Elizabeth Torres
Elizabeth Torres August 11, 2025
A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
Richard Taylor
Richard Taylor September 16, 2025
Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
Matthew Torres
Matthew Torres June 01, 2024
Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
Melissa Allen
Melissa Allen July 18, 2024
Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
Linda Allen
Linda Allen February 18, 2024
Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
Mary Moore
Mary Moore May 17, 2024
Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
Nancy Baker
Nancy Baker May 19, 2024
Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
Rebecca Jackson
Rebecca Jackson August 01, 2025
Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
Lisa  Parker
Lisa Parker December 26, 2024
Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Sandra Scott
Sandra Scott September 25, 2025
A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
Mary Wright
Mary Wright April 01, 2024
Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
Michael Hill
Michael Hill February 06, 2025
Honestly one of the most premium reading experiences lately. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
Joshua Thomas
Joshua Thomas April 01, 2024
Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
Carol Ramirez
Carol Ramirez December 23, 2025
A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
Deborah Allen
Deborah Allen January 27, 2024
A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers.
Edward Rivera
Edward Rivera February 23, 2025
I thoroughly enjoyed the elegance of it. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel.
Nancy  Parker
Nancy Parker February 10, 2025
Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
Edward Rivera
Edward Rivera January 25, 2025
Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
Sarah Sanchez
Sarah Sanchez April 19, 2025
I thoroughly enjoyed the elegance of it. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. I would highly recommend this to discerning readers.
Sharon Roberts
Sharon Roberts April 20, 2024
A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
Cynthia Martin
Cynthia Martin March 12, 2025
Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
Kenneth Lewis
Kenneth Lewis December 22, 2024
Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Ryan Allen
Ryan Allen December 09, 2024
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
Joseph Mitchell
Joseph Mitchell November 21, 2024
Not entirely to my refined tastes. It verged on repetitive in the second act. A more concise edit would have served it well. Perhaps more aligned with a different audience's tastes.
Donna Lewis
Donna Lewis July 27, 2025
Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
Robert Diaz
Robert Diaz July 22, 2024
Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
Jennifer Anderson
Jennifer Anderson December 01, 2024
Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
Patricia Clark
Patricia Clark May 09, 2024
I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. A solid 4 stars from me.
Joshua Brown
Joshua Brown February 09, 2025
I thoroughly enjoyed the elegance of it. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A solid 4 stars from me.
David Rodriguez
David Rodriguez November 29, 2024
Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
Stephanie Nelson
Stephanie Nelson March 29, 2024
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
Sarah Moore
Sarah Moore April 04, 2024
I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
Sandra Walker
Sandra Walker November 08, 2025
Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
Betty Lopez
Betty Lopez September 16, 2024
A very strong entry. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A solid 4 stars from me.
David Lopez
David Lopez December 06, 2025
It was adequate. The prose was competent, yet the characters lacked the depth I usually seek. Unlikely to reread, but a reasonable expenditure of time.
Lisa Martinez
Lisa Martinez February 18, 2024
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
Nicholas Walker
Nicholas Walker February 13, 2025
A decent, if standard, experience. The prose was competent, yet the characters lacked the depth I usually seek. Perfectly average.
Ashley Harris
Ashley Harris April 13, 2024
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
Mary Taylor
Mary Taylor February 16, 2025
Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
Robert Diaz
Robert Diaz February 25, 2024
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
Anthony Carter
Anthony Carter May 16, 2025
Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
Christopher Adams
Christopher Adams January 25, 2025
Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Sharon Scott
Sharon Scott November 08, 2025
I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
Stephanie Martin
Stephanie Martin August 27, 2025
Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers.
Brian Campbell
Brian Campbell October 20, 2025
Took a moment to build, but the payoff was spectacular. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. I would highly recommend this to discerning readers.
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