Topics in Noncommutative Algebra The Theorem of Campbell, Baker, Hau
Motivated by the importance of the Campbell, Baker, Hausdorff, Dynkin Theorem in many different branches of Mathematics and Physics (Lie group-Lie algebra theory, linear PDEs, Quantum and Statistical Mechanics, Numerical Analysis, Theoretical Physics, Con
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For further volumes: http://www.springer.com/series/304
2034
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Andrea Bonfiglioli
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Roberta Fulci
Topics in Noncommutative Algebra The Theorem of Campbell, Baker, Hausdorff and Dynkin
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Andrea Bonfiglioli Roberta Fulci University of Bologna Department of Mathematics Piazza di Porta San Donato 5 40126 Bologna Italy [email protected] [email protected]
ISBN 978-3-642-22596-3 e-ISBN 978-3-642-22597-0 DOI 10.1007/978-3-642-22597-0 Springer Heidelberg Dordrecht London New York Lecture Notes in Mathematics ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 Library of Congress Control Number: 2011937714 Mathematics Subject Classification (2010): 22-XX, 01-XX, 17-XX, 53-XX c Springer-Verlag Berlin Heidelberg 2012 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. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
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Preface
you were asked if the so-called Fundamental Theorem of Algebra is a result of Algebra or of Analysis. What would you answer? And again, among the arguments proving that the complex field is algebraically closed, which would you choose? A proof making use of the concept of continuity? Or of analytic functions, even? Or of Galois theory, instead?
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UPPOSE
The central topic of this book, the mathematical result named after the mathematicians Henry Frederick Baker, John Edward Campbell, Eugene Borisovich Dynkin and Felix Hausdorff, shares – together with the Fundamental Theorem of Algebra – the remarkable property to cross, by its nature, the realms of many mathematical disciplines: Algebra, Analysis, Geometry. As for the proofs of this theorem (named henceforth CBHD, in chronological order of the contributions), it will be evident in due course of the book that the intertwining of Algebra and Analysis is especially discernible: We shall present arguments making use – all at the same time – of topological algebras, the theory of power series, ordinary differential equations techniques, the theory of Lie algebras, metric spaces; and more. If we glance at the fields of application of the CBHD Theorem, it is no surprise that so many different areas are touched upon: the theory of Lie groups and Lie algebras; l
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