Book Description:
This new book is dedicated to recent and important research on Lie groups. A Lie Group is a group which is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure. They are named after the nineteenth century Norwegian mathematician Sophus Lie, who laid the foundations of the theory of continuous transformation groups.

Lie groups represent the best developed theory of continuous symmetry of mathematical objects and structures, which makes them indispensable tools for many parts of contemporary mathematics, as well as for modern theoretical physics. They provide a natural framework for analysing the continuous symmetries of differential equations (Differential Galois theory), in much the same way as permutation groups are used in Galois theory for analysing the discrete symmetries of algebraic equations. An extension of Galois theory to the case of continuous symmetry groups was one of Lie's principal motivations.

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Table of Contents:
Preface

Lie Group Guide to the Universe pp 1-59
(Bernd Schmeikal, Am Platzl 1, Garsten, Austria)

Rotation Manifold SO(3) and Its Tangential Vectors pp 61-88
(Jari Makinen, Tampere Univ. of Technology, Dept. of Mechanics and Design, Tampere, Finland)

Asymptotic Homology of the Quotient of PSL 2(R) by a Modular Group pp 89-122
(Jacques Franchi, I.R.M.A. Univ. Louis Pasteur et CNRS, Descartes, France)

Group Analysis of Solutions of 2-Dimensional Differential Equations pp 123-138
(Sergey I. Senashov, Alexander Yakhno, Univ. de Guadalajara, Univ. Centre of Sciences and Ingeneira, Mexico)

The Module Structure of the Infinite-Dimensional Lie Algebra Attached to a Vector Field pp 139-167
(Guan Keying, Beijing Jiaotong Univ., Beijing, P.R. China)

Lie Group Methods for Modulus Conserving Differential Equations pp 169-186
(Jian-Qiang Sun, Institute of Applied Physics and Computational Mathematics, Beijing, China, Hua Wei, Dept. of Science, Liaoning Technical Univ., Fuxin, China, Gui-Dong Dai, Element Dept., Beijing Institute of Clothing Technology, Beijing, China)

^ Singularities and Stability of A Work Function pp 187-198
(Jean Lerbet, Universit'e d'Evry Val d'Essone, Evry Cedex France)


The Conformal-Affine Structure of Open Quantum Relativity, its Physical Realization and Implications pp 199-265
(G. Basini, Laboratori Nazionali di Frascati, INFN, Frascati, Roma, Italy, S. Capozziello, Dipartimento de Scienze Fisiche, Univ. di Napoli, Napoli, Italy)

^Twisted Balanced Metrics pp 267-281
(Julien Keller, Imperial College, London, UK)

Reduction, Hydrodynamics and Control for Geodesics of Left or Right Invariant Metrics on Lie Groups pp 283-306
(Mikhail V. Deryabin, Mads Clausen Instituttet, Syddansk Universitet, Sønderborg, Denmark)

Some Approximation Theorems for Quasimetric, Induced by Smooth Non-Commutative Vector Fields pp 307-323
(A.V. Greshnov, Institute of Mathematics of Siberian Branch of Russian Academy of Science)

Lie Theory in Physics pp 325-349
(Gabriela P. Ovando, CONICET y ECEN-FCEIA, Univ. Nacional de Rosario, Pellegrini Rosario, Santa Fe, Argentina)

Levy Processes in Lie Groups and Homogeneous Spaces pp 351-383
(Ming Liao, Auburn Univ., Dept. of Mathematics, Auburn Univ., Auburn, AL)

Symmetry Classification of Differential Equations and Reduction Techniques pp 385-399
(Giampaolo Cicogna, Dipartimento di Fisica, dell'Univ. a di Pisa and Istituto Nazionale di Fisica Nucleare, Pisa, Italy)

Deformation and Contraction Schemes for Non-Solvable Real Lie Algebras Up to Dimension Eight pp 401-446
(R. Campoamor-Stursberg, I.M.I., Univ. Complutense de Madrid, Plaza de Ciencias, Madrid, J. Gueron, Intituto de Astronomia y Fisicia del Espacio, UBA-CONICET)

The Automorphism Groups of Some Geometric Structures on Orbifolds pp 447-483
(A.V. Bagaev, N.I. Zhukova, Nizhny Novgorod State Univ. after N.I. Lobachevsky, Nizhny Novgorod, Russia)

Wrap Groups of Connected Fiber Bundles, their Structure and Cohomologies pp 485-561
(S.V. Ludkovsky, Dept. of Applied Mathematics, Moscow State Technical Univ., Moscow, Russia)

Groups of Diffeomorphisms and Wraps of Manifolds Over Non-Archimedean Fields pp 563-600
(S.V. Ludkovsky, Dept. of Applied Mathematics, Moscow State Technical Univ., Moscow, Russia)

Index