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An Introduction to Lie Groups and Lie Algebras (Cambridge Studies in Advanced Mathematics, Series Number 113)

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An Introduction to Lie Groups and Lie Algebras (Cambridge Studies in Advanced Mathematics, Series Number 113)

4.85 81,408 ratings · 6,277 reviews
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Overview: With roots in the nineteenth century, Lie theory has since found many and varied applications in mathematics and mathematical physics, to the point where it is now regarded as a classical branch of mathematics in its own right. This graduate text focuses on the study of semisimple Lie algebras, developing the necessary theory along the way. The material covered ranges from basic definitions of Lie groups to the classification of finite-dimensional representations of semisimple Lie algebras. Written in an informal style, this is a contemporary introduction to the subject which emphasizes the main concepts of the proofs and outlines the necessary technical details, allowing the material to be conveyed concisely. Based on a lecture course given by the author at the State University of New York at Stony Brook, the book includes numerous exercises and worked examples and is ideal for graduate courses on Lie groups and Lie algebras.

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Published July 31, 2008
ISBN 3425581
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Alexander Kirillov Jr Jr
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Alexander Kirillov Jr Jr is the author of several novels. Originally from the East Coast, they now live in the Midwest with family. In addition to writing, Alexander Kirillov Jr Jr enjoys gardening, cooking, and reading way past bedtime. Their work often explores the complexities of everyday life and human relationships.

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Richard Rodriguez
Richard Rodriguez December 04, 2024
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Sarah Evans
Sarah Evans December 13, 2025
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Susan Mitchell November 05, 2025
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James Carter August 23, 2024
Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
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Kevin Ramirez June 23, 2024
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Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Mark Taylor
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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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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.
Joseph Gomez
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Stephanie Flores November 17, 2025
Not entirely to my refined tastes. The prose was competent, yet the characters lacked the depth I usually seek. Suitable if your reading queue is empty.
Emily Scott
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An acceptable diversion. Certain acts were fascinating, while others felt like a slight endeavor to complete. Perhaps more aligned with a different audience's tastes.
Jacob Thomas
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Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
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Took a moment to build, but the payoff was spectacular. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
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Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
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A very strong entry. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall.
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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.
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I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
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Rebecca Baker April 07, 2025
It was adequate. The prose was competent, yet the characters lacked the depth I usually seek. Perfectly average.
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Kevin White June 29, 2024
A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
Rebecca Campbell
Rebecca Campbell March 26, 2025
An acceptable diversion. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Suitable if your reading queue is empty.
David Gonzalez
David Gonzalez May 06, 2024
Took a moment to build, but the payoff was spectacular. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
John Jones
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A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall.
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Brian Walker March 14, 2025
Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
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A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
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Ryan Rodriguez
Ryan Rodriguez June 26, 2025
Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend.
Michelle Scott
Michelle Scott February 13, 2024
Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Thomas Perez
Thomas Perez March 07, 2024
An acceptable diversion. The prose was competent, yet the characters lacked the depth I usually seek. Unlikely to reread, but a reasonable expenditure of time.
William Phillips
William Phillips December 15, 2024
An acceptable diversion. Certain acts were fascinating, while others felt like a slight endeavor to complete. Suitable if your reading queue is empty.
Jennifer Hall
Jennifer Hall January 12, 2024
A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me.
Betty White
Betty White November 12, 2024
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William Nelson
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Patricia Carter
Patricia Carter December 02, 2024
Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
Christopher  Davis
Christopher Davis October 16, 2025
Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
Karen Campbell
Karen Campbell July 14, 2025
Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
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Sarah Lee February 21, 2024
Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
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Christopher Martinez November 05, 2024
A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers.
Robert Green
Robert Green May 19, 2024
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Edward Baker
Edward Baker April 08, 2024
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
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Lisa Lewis August 08, 2025
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall.
Robert King
Robert King July 28, 2025
Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
David Flores
David Flores February 15, 2024
Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
Gary Miller
Gary Miller April 29, 2024
It was adequate. It verged on repetitive in the second act. A more concise edit would have served it well. Suitable if your reading queue is empty.
Lisa Lewis
Lisa Lewis November 19, 2024
A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
Karen Carter
Karen Carter December 03, 2024
Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
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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.
George Thompson
George Thompson March 28, 2025
A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
Donald Allen
Donald Allen December 12, 2025
Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
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Sharon Johnson October 01, 2024
I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
Laura Campbell
Laura Campbell January 26, 2024
Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
Daniel Johnson
Daniel Johnson March 24, 2024
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Linda Evans
Linda Evans July 21, 2025
Not entirely to my refined tastes. It verged on repetitive in the second act. A more concise edit would have served it well. Suitable if your reading queue is empty.
Betty Evans
Betty Evans October 02, 2025
Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
Sarah King
Sarah King January 25, 2025
A decent, if standard, experience. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Unlikely to reread, but a reasonable expenditure of time.
James Carter
James Carter April 10, 2024
Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Robert King
Robert King September 04, 2024
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
Thomas Taylor
Thomas Taylor June 14, 2024
Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
Jacob Johnson
Jacob Johnson November 22, 2025
A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel.
Michael Edwards
Michael Edwards September 24, 2025
I find myself somewhat conflicted. Certain acts were fascinating, while others felt like a slight endeavor to complete. Perhaps more aligned with a different audience's tastes.
Dorothy Cruz
Dorothy Cruz July 23, 2025
Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend.
James Thompson
James Thompson January 12, 2024
Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
John Rodriguez
John Rodriguez April 03, 2025
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
Nancy Taylor
Nancy Taylor May 14, 2025
Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
Michelle Lopez
Michelle Lopez November 14, 2024
Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
Steven Hall
Steven Hall November 15, 2025
A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
Jacob Cruz
Jacob Cruz December 10, 2024
A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
Donald Ramirez
Donald Ramirez July 15, 2024
Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Matthew Rodriguez
Matthew Rodriguez July 26, 2025
Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
Sharon Johnson
Sharon Johnson January 09, 2024
I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
Jennifer Hernandez
Jennifer Hernandez September 12, 2024
I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
Charles Hall
Charles Hall March 15, 2024
A highly sophisticated read. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
William Phillips
William Phillips April 12, 2024
Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Patricia White
Patricia White June 21, 2024
Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
Rebecca Green
Rebecca Green January 20, 2024
A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
Jacob Lee
Jacob Lee December 23, 2025
Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
John Thomas
John Thomas June 11, 2024
Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
Daniel Williams
Daniel Williams July 18, 2024
It was adequate. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Perfectly average.
Brian Carter
Brian Carter September 23, 2025
Excellent, though slightly flawed. It held my rapt attention, even when certain twists were telegraphed. I would highly recommend this to discerning readers.
Paul Roberts
Paul Roberts November 13, 2024
Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Andrew Hill
Andrew Hill February 24, 2024
A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel.
Joshua Taylor
Joshua Taylor April 18, 2025
Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
James Martinez
James Martinez March 17, 2024
A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel.
Elizabeth Williams
Elizabeth Williams January 28, 2025
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
Mark Carter
Mark Carter September 03, 2025
I find myself somewhat conflicted. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Perfectly average.
Stephanie Wright
Stephanie Wright January 25, 2024
A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers.
Sarah Gomez
Sarah Gomez September 17, 2025
I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall.
Rebecca Campbell
Rebecca Campbell January 09, 2024
Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
Donald Gomez
Donald Gomez February 19, 2025
A decent, if standard, experience. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Unlikely to reread, but a reasonable expenditure of time.
Donald Ramirez
Donald Ramirez June 05, 2025
A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall.
Rebecca Gonzalez
Rebecca Gonzalez December 28, 2025
Not entirely to my refined tastes. It verged on repetitive in the second act. A more concise edit would have served it well. Perfectly average.
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