| Abstract Lie Algebras Contributor(s): Winter, David J. (Author) |
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ISBN: 048646282X ISBN-13: 9780486462820 Publisher: Dover Publications OUR PRICE: $10.76 Product Type: Paperback - Other Formats Published: January 2008 Annotation: Solid but concise, this account of Lie algebra emphasizes the theory's simplicity and offers new approaches to major theorems. It also presents a general, extensive treatment of Cartan and related Lie subalgebras over arbitrary fields. Contents include introductory material on prerequisites for modules and basic material on nonassociative algebras. 1972 edition. |
| Additional Information |
| BISAC Categories: - Mathematics | Algebra - Linear - Mathematics | Algebra - Abstract |
| Dewey: 512.482 |
| LCCN: 2007032515 |
| Series: Dover Books on Mathematics |
| Physical Information: 0.31" H x 5.52" W x 8.41" (0.37 lbs) 162 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: Solid but concise, this account of Lie algebra emphasizes the theory's simplicity and offers new approaches to major theorems. Author David J. Winter, a Professor of Mathematics at the University of Michigan, also presents a general, extensive treatment of Cartan and related Lie subalgebras over arbitrary fields. Preliminary material covers modules and nonassociate algebras, followed by a compact, self-contained development of the theory of Lie algebras of characteristic 0. Topics include solvable and nilpotent Lie algebras, Cartan subalgebras, and Levi's radical splitting theorem and the complete reducibility of representations of semisimple Lie algebras. Additional subjects include the isomorphism theorem for semisimple Lie algebras and their irreducible modules, automorphism of Lie algebras, and the conjugacy of Cartan subalgebras and Borel subalgebras. An extensive theory of Cartan and related subalgebras of Lie algebras over arbitrary fields is developed in the final chapter, and an appendix offers background on the Zariski topology. |