Theory of Transformation Groups I General Properties of Continuous T
This modern translation of Sophus Lie's and Friedrich Engel's “Theorie der Transformationsgruppen Band I” will allow readers to discover the striking conceptual clarity and remarkably systematic organizational thought of the original German text. Volume I
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Theory of Transformation Groups I General Properties of Continuous Transformation Groups. A Contemporary Approach and Translation Editor and Translator: Joël Merker
Theory of Transformation Groups I
Sophus Lie
Theory of Transformation Groups I General Properties of Continuous Transformation Groups. A Contemporary Approach and Translation With the collaboration of Friedrich Engel
Editor and Translator: Joël Merker
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Author Sophus Lie (1842–1899)
Editor and Translator Joël Merker Laboratoire de Mathématiques, Faculté des Sciences d’Orsay Université Paris-Sud 11 Orsay France
Collaborator Friedrich Engel (1861–1941)
First edition published in German language by B.G. Teubner, Leipzig, with the title: Theorie der Transformationsgruppen in 1888, 1930 ISBN 978-3-662-46210-2 DOI 10.1007/978-3-662-46211-9
ISBN 978-3-662-46211-9
(eBook)
Library of Congress Control Number: 2015931246 Mathematics Subject Classification: 22E05, 22E10, 22E60, 22-03, 01A05, 01A55, 17B30, 17B40, 17B45, 17B56, 17B66, 17B70, 22F30, 12H05, 14P05, 14P15 Springer Heidelberg New York Dordrecht London © Springer-Verlag Berlin Heidelberg 1888, 1930, 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, 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. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Cover picture taken from “Ny illustreret Tidende”, 1886 Printed on acid-free paper Springer-Verlag GmbH Berlin Heidelberg is part of Springer Science+Business Media (www.springer.com)
THEORIE DER
TRANSFORMATIONSGRUPPEN —————-
ERSTER ABSCHNITT —————UNTER MITWIRKUNG VON Prof. Dr. FRIEDRICH ENGEL
BEARBEITET VON
SOPHUS LIE, WEIL . PROFESSOR DER GEOMETRIE AND DER UNIVERSITÄT LEIPZIG UND PROFESSOR I TRANSFORMASJONSGRUPPENES TEORI AN DER KÖNIGLICHEN FREDERIKS UNIVERSITÄT ZU OSLO
UNVERÄNDERTER NEUDRUCK MIT UNTERSTÜTZUNG DER KÖNIGLICHEN FREDERIKS UNIVERSITÄT ZU OSLO
1930 VERLAG UND DRUCK VON B.G. TEUBNER IN LEIPZIG UND BERLIN
Foreword
This modernized English translation grew out of my old simultaneous interest in the mathematics itself and in the metaphysical thoughts governing its continued developm
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