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Algebra --- Liejeve grupe --- 512.815 --- Symmetric spaces --- Linear representations of Lie groups --- Representations of Lie groups. --- 512.815 Linear representations of Lie groups --- Topological groups. Lie groups --- Lie groups --- Representations of groups --- 512.81 --- 512.81 Lie groups --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Groups, Lie --- Lie algebras --- Topological groups --- Lie groups. --- Representations of Lie groups

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512.81 --- Lie groups --- Lie algebras. --- Einfache Lie-Algebra. --- 512.81 Lie groups --- Lie algebras --- Algebras, Lie --- Algebra, Abstract --- Algebras, Linear

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This is an accessible book on advanced symmetry methods for partial differential equations. Topics include conservation laws, local symmetries, higher-order symmetries, contact transformations, delete "adjoint symmetries," Noether’s theorem, local mappings, nonlocally related PDE systems, potential symmetries, nonlocal symmetries, nonlocal conservation laws, nonlocal mappings, and the nonclassical method. Graduate students and researchers in mathematics, physics, and engineering will find this book useful. This book is a sequel to Symmetry and Integration Methods for Differential Equations (2002) by George W. Bluman and Stephen C. Anco. The emphasis in the present book is on how to find systematically symmetries (local and nonlocal) and conservation laws (local and nonlocal) of a given PDE system and how to use systematically symmetries and conservation laws for related applications.

Ordered algebraic structures --- Topological groups. Lie groups --- Mathematical analysis --- Mathematics --- analyse (wiskunde) --- topologie (wiskunde) --- wiskunde --- topologie

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The aim of this book is to serve both as an introduction to profinite groups and as a reference for specialists in some areas of the theory. The book is reasonably self-contained. Profinite groups are Galois groups. As such they are of interest in algebraic number theory. Much of recent research on abstract infinite groups is related to profinite groups because residually finite groups are naturally embedded in a profinite group. In addition to basic facts about general profinite groups, the book emphasizes free constructions (particularly free profinite groups and the structure of their subgroups). Homology and cohomology is described with a minimum of prerequisites. This second edition contains three new appendices dealing with a new characterization of free profinite groups, presentations of pro-p groups and a new conceptually simpler approach to the proof of some classical subgroup theorems. Throughout the text there are additions in the form of new results, improved proofs, typographical corrections, and an enlarged bibliography. The list of open questions has been updated; comments and references have been added about those previously open problems that have been solved after the first edition appeared.

Number theory --- Group theory --- Ordered algebraic structures --- Topological groups. Lie groups --- Topology --- topologie (wiskunde) --- wiskunde --- getallenleer --- topologie --- Profinite groups

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This book explains recent results in the theory of moving frames that concern the symbolic manipulation of invariants of Lie group actions. In particular, theorems concerning the calculation of generators of algebras of differential invariants, and the relations they satisfy, are discussed in detail. The author demonstrates how new ideas lead to significant progress in two main applications: the solution of invariant ordinary differential equations and the structure of Euler-Lagrange equations and conservation laws of variational problems. The expository language used here is primarily that of undergraduate calculus rather than differential geometry, making the topic more accessible to a student audience. More sophisticated ideas from differential topology and Lie theory are explained from scratch using illustrative examples and exercises. This book is ideal for graduate students and researchers working in differential equations, symbolic computation, applications of Lie groups and, to a lesser extent, differential geometry.

Calculus --- Invariants --- Lie groups --- 512.81 --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Mathematical analysis --- Functions --- Geometry, Infinitesimal --- 512.81 Lie groups --- Calculus of variations. --- Differential equations. --- Geometry, Differential. --- Differential geometry --- 517.91 Differential equations --- Differential equations --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Lie groups. --- Calculus. --- Invariants.