Generalized Lie Theory in Mathematics, Physics and Beyond
The goal of this book is to extend the understanding of the fundamental role of generalizations of Lie theory and related non-commutative and non-associative structures in mathematics and physics. This volume is devoted to the interplay between several ra
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Sergei Silvestrov • Eugen Paal Viktor Abramov • Alexander Stolin Editors
Generalized Lie Theory in Mathematics, Physics and Beyond
ABC
Viktor Abramov Institute of Pure Mathematics University of Tartu J. Liivi 2 50409 Tartu Estonia [email protected]
Sergei Silvestrov (Editor in Chief) Centre for Mathematical Sciences Division of Mathematics Lund Institute of Technology Lund University Box 118 221 00 Lund Sweden [email protected]
Alexander Stolin Mathematical Sciences Chalmers University of Technology and Göteborg University Department of Mathematical Sciences 412 96 Göteborg Sweden [email protected]
Eugen Paal Department of Mathematics Tallinn University of Technology Ehitajate tee 5 19086 Tallinn Estonia [email protected]
ISBN: 978-3-540-85331-2
e-ISBN: 978-3-540-85332-9
Library of Congress Control Number: 2008933563 Math.Subject Classification (2000): 17-06, 16-06, 81-06, 17A-XX, 17B-XX, 81R-XX c 2009 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: WMX Design GmbH, Heidelberg Printed on acid-free paper springer.com
Preface
The aim of this book is to extend the understanding of the fundamental role of generalizations of Lie and related non-commutative and non-associative structures in Mathematics and Physics. This is a thematic volume devoted to the interplay between several rapidly expanding research fields in contemporary Mathematics and Physics, such as generalizations of the main structures of Lie theory aimed at quantization and discrete and non-commutative extensions of differential calculus and geometry, non-associative structures, actions of groups and semi-groups, non-commutative dynamics, noncommutative geometry and applications in Physics and beyond. The specific fields covered by this volume include: • Applications of Lie, non-associative and non-commutative associative structures to generalizations of classical and quantum mechanics and non-linear integrable systems, operadic and group theoretical methods; • Generalizations and quasi-deformations of Lie algebras such as color and super Lie algebras, quasi-Lie algebras, Hom–Lie algebras, infinite-dimensional Lie algebras of vector fields associated to Riemann surfaces, quasi-Lie a
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