The theory of Lie algebras and algebraic groups has been an area of active research in the last 50 years. It intervenes in many different areas of mathematics : for example invariant theory, Poisson geometry, harmonic analysis, mathematical physics. The aim of this book is to assemble in a single volume the algebraic aspects of the theory so as to present the foundation of the theory in characteristic zero. Detailed proofs are included and some recent results are discussed in the last chapters. All the prerequisites on commutative algebra and algebraic geometry are included.
Springer Monographs in Mathematics
Patrice Tauvel Rupert W. T. Yu
Lie Algebras and Algebraic Groups With 44 Figures
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Patrice Tauvel Rupert W. T. Yu Département de Mathématiques Université de Poitiers Boulevard Marie et Pierre Curie, Téléport 2 – BP 30179 86962 Futuroscope Chasseneuil cedex, France e-mail:
[email protected] [email protected]
Library of Congress Control Number: 2005922400
Mathematics Subject Classification (2000): 17-01, 17-02, 17Bxx, 20Gxx ISSN 1439-7382 ISBN-10 3-540-24170-1 Springer Berlin Heidelberg New York ISBN-13 978-3-540-24170-6 Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the