Lie Groups, Lie Algebras, and Representations An Elementary Introduction /

• Κύριος συγγραφέας: Hall, Brian C. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2015.
• Έκδοση: Second Edition.
• Σειρά: Graduate Texts in Mathematics, 222
• Θέματα: Mathematics.; Nonassociative rings.; Rings (Algebra).; Topological groups.; Lie groups.; Manifolds (Mathematics).; Complex manifolds.; Topological Groups, Lie Groups.; Non-associative Rings and Algebras.; Manifolds and Cell Complexes (incl. Diff.Topology).

This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for pro...

Πίνακας περιεχομένων:

• Part I: General Theory.-Matrix Lie Groups
• The Matrix Exponential
• Lie Algebras
• Basic Representation Theory
• The Baker–Campbell–Hausdorff Formula and its Consequences
• Part II: Semisimple Lie Algebras
• The Representations of sl(3;C).-Semisimple Lie Algebras.- Root Systems
• Representations of Semisimple Lie Algebras
• Further Properties of the Representations
• Part III: Compact lie Groups
• Compact Lie Groups and Maximal Tori
• The Compact Group Approach to Representation Theory
• Fundamental Groups of Compact Lie Groups
• Appendices.