Lie Algebras by Shlomo Sternberg

About this book :-
Shlomo Sternberg’s Lie Algebras is a book that dives deep into the world of Lie algebras, important in both mathematics and physics. It’s not just a list of formulas. It’s a comprehensive guide to how Lie algebras are structured and how they show up in the world around us. The book is deep and technical, so it’s best suited for students with a solid background in mathematics (like linear algebra and abstract algebra). This book addresses the following topics: The Campbell Baker Hausdorff formula, sl(2) and its representations, classical simple algebras, Engel-Lie-Cartan-Weyl, conjugacy of Cartan subalgebras, simple finite dimensional algebras, cyclic highest weight modules, Serre’s theorem, Clifford algebras and spin representations, Kostant Dirac operator, the center of U(g).

Book Detail :-
Title: Lie Algebras by Shlomo Sternberg
Publisher: Shlomo ternberg
Year: 2004
Pages: 198
Type: PDF
Language: English
ISBN-10 #: N/A
ISBN-13 #: N/A
License: Linked Content Owned by Author
Amazon: Amazon

About Author :-
The author Shlomo Zvi Sternberg (1936 – 2024) was an American mathematician and Professor at Department of Mathematics at Harvard University. He was known for his work in geometry, particularly symplectic geometry and Lie theory. He earned his PhD from Johns Hopkins University in 1955, with a thesis entitled Some Problems in Discrete Nonlinear Transformations in One and Two Dimensions, supervised by Aurel Wintner. After postdoctoral work at New York University (1956–1957) and an instructorship at University of Chicago (1957–1959), Sternberg joined the Mathematics Department at Harvard University in 1959, where he was George Putnam Professor of Pure and Applied Mathematics until 2017. Since 2017, he was Emeritus Professor at the Harvard Mathematics Department. Sternberg was well-known because of his PhD thesis, is known as the "Sternberg linearization theorem" which asserts that a smooth map near a hyperbolic fixed point can be made linear by a smooth change of coordinates provided that certain non-resonance conditions are satisfied. He also proved generalizations of the Birkhoff canonical form theorems for volume preserving mappings in n-dimensions and symplectic mappings, all in the smooth case. In the 1960s, Sternberg became involved with Isadore Singer in the project of revisiting Élie Cartan's papers. Sternberg also contribut to the topic of Lie group actions on symplectic manifolds, in particular involving various aspects of the theory of symplectic reduction. His contributions to symplectic geometry and Lie theory have also included a number of basic textbooks on these subjects, among them the three graduate level texts with Victor Guillemin: "Geometric Asymptotics," "Symplectic Techniques in Physics", and "Semi-Classical Analysis".

Book Contents :-
1. The Campbell Baker Hausdorff Formula 2. sl(2) and its Representations 3. The classical simple algebras 4. Engel-Lie-Cartan-Weyl 5. Conjugacy of Cartan subalgebras 6. The simple finite dimensional algebras 7. Cyclic highest weight modules 8. Serre’s theorem 9. Clifford algebras and spin representations 10. The Kostant Dirac operator 11. The center of U (g)

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