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Introduction to Lie Algebras

Buch | Softcover
251 Seiten
2006
Springer London Ltd (Verlag)
978-1-84628-040-5 (ISBN)

Lese- und Medienproben

Introduction to Lie Algebras - K. Erdmann, Mark J. Wildon
CHF 52,40 inkl. MwSt
Lie groups and Lie algebras have become essential to many parts of mathematics and theoretical physics, with Lie algebras a central object of interest in their own right.



This book provides an elementary introduction to Lie algebras based on a lecture course given to fourth-year undergraduates.
Lie groups and Lie algebras have become essential to many parts of mathematics and theoretical physics, with Lie algebras a central object of interest in their own right.





This book provides an elementary introduction to Lie algebras based on a lecture course given to fourth-year undergraduates. The only prerequisite is some linear algebra and an appendix summarizes the main facts that are needed. The treatment is kept as simple as possible with no attempt at full generality. Numerous worked examples and exercises are provided to test understanding, along with more demanding problems, several of which have solutions.





Introduction to Lie Algebras covers the core material required for almost all other work in Lie theory and provides a self-study guide suitable for undergraduate students in their final year and graduate students and researchers in mathematics and theoretical physics.

Karin Erdmann is a well-known and respected algebraist at the international level, with extensive experience in writing and teaching.

Ideals and Homomorphisms.- Low-Dimensional Lie Algebras.- Solvable Lie Algebras and a Rough Classification.- Subalgebras of gl(V).- Engel’s Theorem and Lie’s Theorem.- Some Representation Theory.- Representations of sl(2, C).- Cartan’s Criteria.- The Root Space Decomposition.- Root Systems.- The Classical Lie Algebras.- The Classification of Root Systems.- Simple Lie Algebras.- Further Directions.- Appendix A: Linear Algebra.- Appendix B: Weyl’s Theorem.- Appendix C: Cartan Subalgebras.- Appendix D: Weyl Groups.- Appendix E: Answers to Selected Exercises.

Erscheint lt. Verlag 7.9.2011
Reihe/Serie Springer Undergraduate Mathematics Series
Zusatzinfo XII, 251 p.
Verlagsort England
Sprache englisch
Maße 178 x 235 mm
Themenwelt Mathematik / Informatik Mathematik Algebra
Naturwissenschaften Physik / Astronomie
Schlagworte Liesche Algebren/Gruppen
ISBN-10 1-84628-040-0 / 1846280400
ISBN-13 978-1-84628-040-5 / 9781846280405
Zustand Neuware
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