Lie groups : new research
著者
書誌事項
Lie groups : new research
（Mathematics research developments series）
Nova Science Publishers, c2009
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注記
Includes bibliographical reference and indx
内容説明・目次
内容説明
This 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.
目次
- Preface
- Lie Group Guide to the Universe
- Asymptotic Homology of the Quotient of PSL 2(R) by a Modular Group
- Processes in Lie Groups and Homogeneous Spaces
- Group Analysis of Solutions of 2-Dimensional Differential Equations
- The Module Structure of the Infinite-Dimensional Lie Algebra Attached to a Vector Field
- Lie Group Methods for Modulus Conserving Differential Equations
- Symmetry Classification of Differential Equations and Reduction Techniques
- Deformation and Contraction Schemes for Non-Solvable Real Lie Algebras Up to Dimension Eight
- The Automorphism Groups of Some Geometric Structures on Orbifolds
- Wrap Groups of Connected Fiber Bundles, their Structure and Cohomologies
- Groups of Diffeomorphisms and Wraps of Manifolds Over Non-Archimedean Fields
- The Conformal-Affine Structure of Open Quantum Relativity, its Physical Realization and Implications
- Twisted Balanced Metrics
- Reduction, Hydrodynamics and Control for Geodesics of Left or Right Invariant Metrics on Lie Groups
- Rotation Manifold SO(3) and Its Tangential Vectors
- Some Approximation Theorems for Quasimetric, Induced by Smooth Non-Commutative Vector Fields
- Lie Theory in Physics
- Index.
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