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Lie algebras and representation theory by Dietrich Burde
This note covers basic notions of lie algebra theory, Structure theory of lie algebras, Representations of semi simple lie algebras.
Author(s): Dietrich Burde
113 Pages
Lie Algebras and Their Representations
This note explains the following topics: Representations of sl2, Structure and classification of simple lie algebras, Structure theory of semisimple lie algebras and root systems.
Author(s): University of Cambridge
34 Pages
Lie Algebras by Brooks Roberts
This note covers the following topics: Solvable and nilpotent Lie algebras, The theorems of Engel and Lie, representation theory, Cartan’s criteria, Weyl’s theorem, Root systems, Cartan matrices and Dynkin diagrams, The classical Lie algebras, Representation theory.
Author(s): Brooks Roberts
217 Pages
Introduction to Lie Groups by Alistair Savage
This note focus on the so-called matrix Lie groups since this allows us to cover the most common examples of Lie groups in the most direct manner and with the minimum amount of background knowledge. Topics covered includes: Matrix Lie groups, Topology of Lie groups, Maximal tori and centres, Lie algebras and the exponential map, Covering groups.
Author(s): Alistair Savage
111 Pages
Lie Groups Representation Theory and Symmetric Spaces
This note covers the following topics: Fundamentals of Lie Groups, A Potpourri of Examples, Basic Structure Theorems, Complex Semisimple Lie algebras, Representation Theory, Symmetric Spaces.
Author(s): Wolfgang Ziller
178 Pages
In these lectures we will start from the beginning the theory of Lie algebras and their representations. Topics covered includes: General properties of Lie algebras, Jordan-Chevalley decomposition, semisimple Lie algebras, Classification of complex semisimple Lie algebras, Cartan subalgebras, classification of connected Coxeter graphs and complex semisimple Lie algebras, Poicare-Birkhoff-Witt theorem.
Author(s): Prof. Dr. Nicolas Perrin
NA Pages
Introduction to Lie Groups and Lie Algebras
This book covers the following topics: Lie Groups:Basic Definitions, Lie algebras, Representations of Lie Groups and Lie Algebras, Structure Theory of Lie Algebras, Complex Semisimple Lie Algebras, Root Systems, Representations of Semisimple Lie Algebras, Root Systems and Simple Lie Algebras.
Author(s): Alexander Kirillov
177 Pages
Lecture Notes on Lie Algebras and Lie Groups
This book covers the following topics: Elements of Group Theory, Lie Groups and Lie Algebras, Representation theory.
Author(s): Luiz Agostinho Ferreira
150 Pages
