Lie Algebras (Dover Books on Mathematics) - Softcover
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, Cartan’s criterion and its consequences, and split semi-simple 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 Ado-Iwasawa, classification of irreducible modules, and characters of the irreducible modules. In Chapter 9 the automorphisms of semi-simple 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 well-known 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 self-study.
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, Cartan’s criterion and its consequences, and split semi-simple 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 Ado-Iwasawa, classification of irreducible modules, and characters of the irreducible modules. In Chapter 9 the automorphisms of semi-simple 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 well-known 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 self-study.
"synopsis" may belong to another edition of this title.
About the Author:
One of the world's leading researchers in abstract algebra, Nathan Jacobson (1910-95) taught at several prominent universities, including the University of Chicago, Johns Hopkins, and Yale.
"About this title" may belong to another edition of this title.
- PublisherDover Publications
- Publication date1979
- ISBN 10 0486638324
- ISBN 13 9780486638324
- BindingPaperback
- Number of pages352
- Rating
Buy New
Learn more about this copy
US$ 11.19
Shipping:
US$ 3.99
Within U.S.A.
Top Search Results from the AbeBooks Marketplace
Stock Image
Lie Algebras Format: Paperback
Published by
Dover Publishers
(1979)
ISBN 10: 0486638324
ISBN 13: 9780486638324
New
Softcover
Quantity: > 20
Seller:
Rating
Book Description Condition: New. Brand New. Seller Inventory # 0486638324
Buy New
US$ 11.19
Convert currency
Stock Image
Lie Algebras (Dover Books on Mathematics)
Published by
Dover Publications
(1979)
ISBN 10: 0486638324
ISBN 13: 9780486638324
New
Softcover
Quantity: 1
Seller:
Rating
Book Description Condition: New. Book is in NEW condition. Seller Inventory # 0486638324-2-1
Buy New
US$ 24.74
Convert currency
Stock Image
Lie Algebras (Dover Books on Mathematics)
Published by
Dover Publications
(1979)
ISBN 10: 0486638324
ISBN 13: 9780486638324
New
Softcover
Quantity: 1
Seller:
Rating
Book Description Condition: New. New! This book is in the same immaculate condition as when it was published. Seller Inventory # 353-0486638324-new
Buy New
US$ 24.75
Convert currency
Stock Image
Lie Algebras (Dover Books on Mathematics)
Published by
Dover Publications
(1979)
ISBN 10: 0486638324
ISBN 13: 9780486638324
New
Softcover
Quantity: 1
Seller:
Rating
Book Description Softcover. Condition: New. 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 semi-simple 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 Ado-Iwasawa, classification of irreducible modules, and characters of the irreducible modules. In Chapter 9 the automorphisms of semi-simple 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 well-known 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 self-study. Seller Inventory # DADAX0486638324
Buy New
US$ 24.78
Convert currency
Stock Image
Lie Algebras (Dover Books on Mathematics)
Published by
Dover Publications
(1979)
ISBN 10: 0486638324
ISBN 13: 9780486638324
New
Paperback
Quantity: 1
Seller:
Rating
Book Description Paperback. Condition: new. New. Fast Shipping and good customer service. Seller Inventory # Holz_New_0486638324
Buy New
US$ 21.83
Convert currency
Stock Image
Lie Algebras (Dover Books on Mathematics)
Published by
Dover Publications
(1979)
ISBN 10: 0486638324
ISBN 13: 9780486638324
New
Softcover
Quantity: 1
Seller:
Rating
Book Description Condition: new. Seller Inventory # FrontCover0486638324
Buy New
US$ 29.58
Convert currency
Stock Image
Lie Algebras
Published by
Dover Pubns
(1979)
ISBN 10: 0486638324
ISBN 13: 9780486638324
New
Paperback
Quantity: 1
Seller:
Rating
Book Description Paperback. Condition: Brand New. 331 pages. 8.25x5.75x0.75 inches. In Stock. Seller Inventory # 0486638324
Buy New
US$ 37.20
Convert currency
Stock Image
Lie Algebras
Published by
Dover Publications Inc.
(1979)
ISBN 10: 0486638324
ISBN 13: 9780486638324
New
Softcover
Quantity: 1
Seller:
Rating
Book Description Condition: new. Book is in NEW condition. Satisfaction Guaranteed! Fast Customer Service!!. Seller Inventory # PSN0486638324
Buy New
US$ 21.78
Convert currency
Stock Image
Lie Algebras (Dover Books on Mathematics)
Published by
Dover Publications
(1979)
ISBN 10: 0486638324
ISBN 13: 9780486638324
New
Paperback
Quantity: 1
Seller:
Rating
Book Description Paperback. Condition: new. New. Seller Inventory # Wizard0486638324
Buy New
US$ 51.61
Convert currency
Stock Image
Lie Algebras (Dover Books on Mathematics)
Published by
Dover Publications
(1979)
ISBN 10: 0486638324
ISBN 13: 9780486638324
New
Paperback
Quantity: 1
Seller:
Rating
Book Description Paperback. Condition: new. New Copy. Customer Service Guaranteed. Seller Inventory # think0486638324
Buy New
US$ 51.35
Convert currency