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Drawing on a wide range of mathematical disciplines, including geometry, analysis, applied mathematics and algebra, this book presents an innovative synthesis of methods used to study problems of equivalence and symmetry which arise in a variety of mathematical fields and physical applications. Systematic and constructive methods for solving equivalence problems and calculating symmetries are developed and applied to a wide variety of mathematical systems, including differential equations, variational problems, manifolds, Riemannian metrics, polynomials and differential operators. Particular emphasis is given to the construction and classification of invariants, and to the reductions of complicated objects to simple canonical forms. This book will be a valuable resource for students and researchers in geometry, analysis, algebra, mathematical physics and other related fields.

Geometry, Differential. --- Invariants. --- Symmetry (Physics)

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This volume introduces mathematicians and physicists to a crossing point of algebra, physics, differential geometry and complex analysis. The book follows the French tradition of Cartan, Chevalley and Crumeyrolle and summarizes Crumeyrolle's own work on exterior algebra and spinor structures. The depth and breadth of Crumeyrolle's research interests and influence in the field is investigated in a number of articles. Of interest to physicists is the modern presentation of Crumeyrolle's approach to Weyl spinors, and to his spinoriality groups, which are formulated with spinor operators of Kustaanheimo and Hestenes. The Dirac equation and Dirac operator are studied both from the complex analytic and differential geometric points of view, in the modern sense of Ryan and Trautman. For mathematicians and mathematical physicists whose research involves algebra, quantum mechanics and differential geometry.

Clifford algebras. --- Functions of complex variables. --- Geometry, Differential. --- Mathematical physics. --- Spinor analysis. --- Crumeyrolle, Albert,

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Geometry [Differential ] --- Meetkunde [Differentiaal] --- Geometry, Differential --- #WWIS:didaktiek --- 514.75 --- 514.76 --- 514.76 Geometry of differentiable manifolds and of their submanifolds --- Geometry of differentiable manifolds and of their submanifolds --- 514.75 Differential geometry in spaces with fundamental groups --- Differential geometry in spaces with fundamental groups --- Differential geometry --- Differential geometry. Global analysis --- Geometry, Differential.

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Differential geometry. Global analysis --- Geometry, Riemannian. --- Geodesics (Mathematics) --- Géométrie de Riemann. --- Géodésiques (mathématiques) --- Geometry, Riemannian --- Riemann geometry --- Riemannian geometry --- Generalized spaces --- Geometry, Non-Euclidean --- Semi-Riemannian geometry --- Geometry, Differential --- Global analysis (Mathematics) --- Mathematics

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515.1 --- 515.1 Topology --- Topology --- Topologie différentielle --- Topological manifolds --- 514 --- 514 Geometry --- Geometry --- Differential topology --- 515.16 --- Geometry, Differential --- 515.16 Topology of manifolds --- Topology of manifolds --- Topologie différentielle