Lie Algebras by Nathan Jacobson
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About this book :-
Lie Algebras written by
Definitive treatment covers split semi-simple Lie algebras, universal enveloping algebras, classification of irreducible modules, automorphisms, simple Lie algebras over an arbitrary field, and more. Classic handbook for researchers and students; useable in graduate courses or for self-study.
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 textbook for graduate courses.
The present book is based on lectures which the author has given at Yale during the past ten years, especially those given during the academic year 1959-1960. It is primarily a textbook to be studied by students on their own or to be used for a course on Lie algebras. Besides the usual general knowledge of algebraic concepts, a good acquaintance with linear algebra (linear transformations, bilinear forms, tensor products) is presupposed. Moreover, this is about all the equipment needed for an understanding of the first nine chapters. For the tenth chapter, we require also a knowledge of the notions of Galois theory and some of the results of the Wedderburn structure theory of associative algebras. The subject of Lie algebras has much to recommend it as a .subject for study immediately following courses on general abstract algebra and linear algebra, both because of the beauty of its results and its structure, and because of its many contacts with other branches of mathematics (group theory, differential geometry, differential equations, topology). In this exposition we'have tried to avoid rnaking the treatment too abstract and have consistently followed the point of view of treating the theory as a branch of linear algebra.
Book Detail :-
Title: Lie Algebras
Author(s): Nathan Jacobson
Publisher: Dover Publications
Series: Dover Books on Advanced Mathematics
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About Author :-
Author Nathan Jacobson (1910–1999) was an American mathematician. Nachman Arbiser in Warsaw, Jacobson emigrated to America with his family in 1918. Recognized as one of the leading algebraists of his generation, he wrote more than a dozen standard textbooks. He graduated from the University of Alabama in 1930 and was awarded a doctorate in mathematics from Princeton University in 1934. While working on his thesis, Non-commutative polynomials and cyclic algebras, he was advised by Joseph Wedderburn. Jacobson taught and researched at Bryn Mawr College (1935–1936), the University of Chicago (1936–1937), the University of North Carolina at Chapel Hill (1937–1943), and Johns Hopkins University (1943–1947) before joining Yale University in 1947. He remained at Yale until his retirement.
Nathan Jacobson is from Yale University, Department of Mathematics, New Haven Connecticut.
All Famous Books of this Author :-
Here is list all books/editions avaliable of this author, We recomended you to download all.
1. Basic Algebra I (2E) by Nathan Jacobson
2. Basic Algebra II (2E) by Nathan Jacobson
3. PI Algebras An Introduction by Nathan Jacobson
4. Structure and Representations of Jordan Algebras by Nathan Jacobson
5. Lectures On Quadratic Jordan Algebras by Nathan Jacobson
6. Lie Algebras by Nathan Jacobson
7. Lectures in Abstract Algebra: II. Linear Algebra by Nathan Jacobson
8. Lectures in Abstract Algebra, Volume III: Theory of Fields and Galois Theory by Nathan Jacobson
9. The Theory of Rings by Nathan Jacobson
10. Finite Dimensional Division Algebras by Nathan Jacobson
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Book Contents :-
Lie Algebras written by
cover the following topics.
1. Basic Concepts
2. Solvable and Nilpotent Lie Algebras
3. Cartan's Criterion and Its Consequences
4. Split Semi-simple Lie Algebras
5. Universal Envetoping Algebras
6. The Theorem of Ado-Iwasawa
7. Characterg of the lrreducible Modules
8. Characterg of the lrreducible Modules
10. Simple Lie Algebras oyer an Arbitrary Field
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