Lie Algebras (Dover Books On Mathematics)

Lie Algebras (Dover Books On Mathematics)

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Lie Group Theory, Developed By M. Sophus Lie In The Nineteenth Century, Ranks Among The More Important Developments In Modern Mathematics. Lie Algebras Comprise A Significant Part Of Lie Group Theory And Are Being Actively Studied Today. This Book, By Professor Nathan Jacobson Of Yale, Is The Definitive Treatment Of The Subject And Can Be Used As A Text For Graduate Courses.Chapter 1 Introduces Basic Concepts That Are Necessary For An Understanding Of Structure Theory, While The Following Three Chapters Present The Theory Itself: Solvable And Nilpotent Lie Algebras, Cartans Criterion And Its Consequences, And Split Semisimple Lie Algebras. Chapter 5, On Universal Enveloping Algebras, Provides The Abstract Concepts Underlying Representation Theory. The Basic Results On Representation Theory Are Given In Three Succeeding Chapters: The Theorem Of Adoiwasawa, Classification Of Irreducible Modules, And Characters Of The Irreducible Modules. In Chapter 9 The Automorphisms Of Semisimple Lie Algebras Over An Algebraically Closed Field Of Characteristic Zero Are Determined. These Results Are Applied In Chapter 10 To The Problems Of Sorting Out The Simple Lie Algebras Over An Arbitrary Field. The Reader, To Fully Benefit From This Tenth Chapter, Should Have Some Knowledge About The Notions Of Galois Theory And Some Of The Results Of The Wedderburn Structure Theory Of Associative Algebras.Nathan Jacobson, Presently Henry Ford Ii Professor Of Mathematics At Yale University, Is A Wellknown Authority In The Field Of Abstract Algebra. His Book, Lie Algebras, Is A Classic Handbook Both For Researchers And Students. Though It Presupposes Knowledge Of Linear Algebra, It Is Not Overly Theoretical And Can Be Readily Used For Selfstudy.

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Frequently Asked Questions

  • Q: What is the main focus of 'Lie Algebras' by Nathan Jacobson? A: The book primarily focuses on the theory of Lie algebras, a significant aspect of Lie group theory, providing a comprehensive treatment suitable for graduate-level courses.
  • Q: Who is the intended audience for this book? A: The intended audience includes graduate students and researchers in the field of mathematics, particularly those with an interest in abstract algebra and Lie theory.
  • Q: What topics are covered in the book's chapters? A: The book covers fundamental concepts of Lie algebras, solvable and nilpotent Lie algebras, Cartan’s criterion, universal enveloping algebras, and representation theory, among other advanced topics.
  • Q: Does this book require prior knowledge of mathematics? A: Yes, while it is accessible for self-study, it presupposes some knowledge of linear algebra and basic algebraic structures.
  • Q: What is the publication date of 'Lie Algebras'? A: The book was published on December 1, 1979.
  • Q: What is the format of the book? A: The book is available in a paperback binding, making it suitable for both personal use and academic settings.
  • Q: How many pages does 'Lie Algebras' have? A: The book contains a total of 352 pages.
  • Q: Who is the author of 'Lie Algebras'? A: The book is authored by Nathan Jacobson, a noted professor of mathematics at Yale University.
  • Q: Is this book suitable for self-study? A: Yes, 'Lie Algebras' is designed to be a classic handbook that can be used for self-study, despite its academic rigor.
  • Q: What makes this book a definitive treatment of Lie algebras? A: Its comprehensive coverage of essential concepts, detailed explanations, and the author's expertise in the field establish it as a definitive text for understanding Lie algebras.