Algebraic Groups and Lie Groups with Few Factors
Algebraic groups are treated in this volume from a group theoretical point of view and the obtained results are compared with the analogous issues in the theory of Lie groups. The main body of the text is devoted to a classification of algebraic groups an
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Alfonso Di Bartolo Giovanni Falcone Peter Plaumann Karl Strambach
Algebraic Groups and Lie Groups with Few Factors
1944
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Lecture Notes in Mathematics Editors: J.-M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris
1944
Alfonso Di Bartolo · Giovanni Falcone Peter Plaumann · Karl Strambach
Algebraic Groups and Lie Groups with Few Factors
123
Authors Alfonso Di Bartolo Dipartimento di Matematica e Applicazioni Università degli Studi di Palermo via Archirafi 34 90123 Palermo Italy [email protected]
Giovanni Falcone
Peter Plaumann Karl Strambach Mathematisches Institut Bismarckstrasse 1 1/2 91054 Erlangen Germany [email protected] [email protected]
Dipartimento di Metodi e Modelli Matematici Università degli Studi di Palermo Viale delle Scienze Ed. 8 90138 Palermo Italy [email protected]
ISBN: 978-3-540-78583-5 e-ISBN: 978-3-540-78584-2 DOI: 10.1007/978-3-540-78584-2 Lecture Notes in Mathematics ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 Library of Congress Control Number: 2008921922 Mathematics Subject Classification (2000): 20G10, 14L10, 22E25, 17B30, 20E15 c 2008 Springer-Verlag Berlin Heidelberg ° 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 provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: WMXDesign GmbH Printed on acid-free paper 987654321 springer.com
Preface
In the theory of locally compact topological groups, the aspects and notions from abstract group theory have conquered a meaningful place from the beginning (see New Bibliography in [44] and, e.g. [41–43]). Imposing grouptheoretical conditions on the closed connected subgroups of a topological group has always been the way to develop the theory of locally compact groups along the lines of the theory of abstract groups. Despite the fact that the class of algebraic groups has become a classical object in the mathematics of the last decades, most of the attention was concentrated on reductive algebraic groups. For an affine connected solvable algebraic group G, the theorem of Lie–Kolchin has been considered as definitive for the structure of G, whereas for connected non-affine groups, the attention turns to the analytic and homological aspects of these groups, which are quasi-projective varieties (cf. [79, 80, 89]). Complex Lie groups a
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