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ISBN: 1400883857 Year: 2016 Publisher: Princeton, NJ : Princeton University Press,
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This famous book was the first treatise on Lie groups in which a modern point of view was adopted systematically, namely, that a continuous group can be regarded as a global object. To develop this idea to its fullest extent, Chevalley incorporated a broad range of topics, such as the covering spaces of topological spaces, analytic manifolds, integration of complete systems of differential equations on a manifold, and the calculus of exterior differential forms. The book opens with a short description of the classical groups: unitary groups, orthogonal groups, symplectic groups, etc. These special groups are then used to illustrate the general properties of Lie groups, which are considered later. The general notion of a Lie group is defined and correlated with the algebraic notion of a Lie algebra; the subgroups, factor groups, and homomorphisms of Lie groups are studied by making use of the Lie algebra. The last chapter is concerned with the theory of compact groups, culminating in Peter-Weyl's theorem on the existence of representations. Given a compact group, it is shown how one can construct algebraically the corresponding Lie group with complex parameters which appears in the form of a certain algebraic variety (associated algebraic group). This construction is intimately related to the proof of the generalization given by Tannaka of Pontrjagin's duality theorem for Abelian groups. The continued importance of Lie groups in mathematics and theoretical physics make this an indispensable volume for researchers in both fields.
Continuous groups. --- Additive group. --- Adjoint representation. --- Algebra over a field. --- Algebraic extension. --- Algebraic variety. --- Algebraically closed field. --- Analytic function. --- Analytic manifold. --- Automorphism. --- Axiom of countability. --- Ball (mathematics). --- Cardinal number. --- Characteristic polynomial. --- Coefficient. --- Commutator subgroup. --- Complex number. --- Connected component (graph theory). --- Continuous function (set theory). --- Continuous function. --- Coordinate system. --- Coset. --- Countable set. --- Covering group. --- Covering space. --- Differential algebra. --- Differential calculus. --- Differential form. --- Differential of a function. --- Dual space. --- Eigenvalues and eigenvectors. --- Endomorphism. --- Equivalence class. --- Existential quantification. --- Exponential function. --- Exterior algebra. --- Fundamental group. --- Galois group. --- General topology. --- Geometry. --- Group (mathematics). --- Group theory. --- Hermitian matrix. --- Homeomorphism. --- Homogeneous space. --- Homomorphism. --- Homotopy group. --- Identity element. --- Identity matrix. --- Infinitesimal transformation. --- Integer. --- Invariant subspace. --- Irreducible representation. --- Kronecker product. --- Lie algebra. --- Lie group. --- Linear function. --- Linear map. --- Linear space (geometry). --- Linear subspace. --- Linearization. --- Locally connected space. --- Manifold. --- Mathematical induction. --- Matrix exponential. --- Modular arithmetic. --- Module (mathematics). --- Monodromy. --- Morphism. --- Open set. --- Orthogonal group. --- Parametric equation. --- Permutation. --- Power series. --- Projective plane. --- Real number. --- Regular matrix. --- Representation theory. --- Riemann surface. --- Simply connected space. --- Skew-symmetric matrix. --- Special case. --- Subalgebra. --- Subgroup. --- Submanifold. --- Subset. --- Summation. --- Symplectic geometry. --- Symplectic group. --- Tangent space. --- Theorem. --- Topological group. --- Topological space. --- Topology. --- Trigonometric polynomial. --- Union (set theory). --- Uniqueness theorem. --- Unitary group. --- Unitary matrix. --- Variable (mathematics). --- Vector space.
Book
ISBN: 0691042225 1306989531 1400853060 0691616140 9781400853069 0691643466 9780691042220 Year: 1980 Volume: 7 Publisher: Princeton, N.J. Princeton University Press
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The utility idea has had a long history in economics, especially in the explanation of demand and in welfare economics. In a comprehensive survey and critique of the Slutsky theory and the pattern to which it belongs in the economic context, S. N. Afriat offers a resolution of questions central to its main idea, including sufficient conditions as well.Originally published in 1980.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Demand functions (Economic theory) --- Utility theory --- 330.105 --- 338.5 --- Demand (Economic theory) --- Value --- Revealed preference theory --- Demand curves (Economic theory) --- Functions, Demand (Economic theory) --- Economics --- 330.105 Wiskundige economie. Wiskundige methoden in de economie --- Wiskundige economie. Wiskundige methoden in de economie --- 338.5 Prijsvorming. Prijskostenverhouding. Prijsbeweging. Prijsfluctuatie--macroeconomisch; prijsindex zie {336.748.12} --- Prijsvorming. Prijskostenverhouding. Prijsbeweging. Prijsfluctuatie--macroeconomisch; prijsindex zie {336.748.12} --- Mathematical models --- Quantitative methods (economics) --- E-books --- Utility theory. --- DEMAND FUNCTIONS (Economic theory) --- Adjoint. --- Aggregate supply. --- Arrow's impossibility theorem. --- Axiom. --- Big O notation. --- Bruno de Finetti. --- Chain rule. --- Coefficient. --- Commodity. --- Concave function. --- Continuous function. --- Convex cone. --- Convex function. --- Convex set. --- Corollary. --- Cost curve. --- Cost-effectiveness analysis. --- Cost–benefit analysis. --- Counterexample. --- Demand curve. --- Derivative. --- Determinant. --- Differentiable function. --- Differential calculus. --- Differential equation. --- Differential form. --- Divisia index. --- Economic equilibrium. --- Economics. --- Einstein notation. --- Equivalence relation. --- Explicit formulae (L-function). --- Factorization. --- Frobenius theorem (differential topology). --- Function (mathematics). --- Functional equation. --- General equilibrium theory. --- Heine–Borel theorem. --- Hessian matrix. --- Homogeneous function. --- Idempotence. --- Identity (mathematics). --- Identity matrix. --- Inequality (mathematics). --- Inference. --- Infimum and supremum. --- Integrating factor. --- Interdependence. --- Interval (mathematics). --- Inverse demand function. --- Inverse function theorem. --- Inverse function. --- Invertible matrix. --- Lagrange multiplier. --- Lagrangian (field theory). --- Lagrangian. --- Law of demand. --- Limit point. --- Line segment. --- Linear function. --- Linear inequality. --- Linear map. --- Linearity. --- Logical disjunction. --- Marginal cost. --- Mathematical induction. --- Mathematical optimization. --- Maxima and minima. --- Monotonic function. --- Ordinary differential equation. --- Orthogonal complement. --- Oskar Morgenstern. --- Pareto efficiency. --- Partial derivative. --- Permutation. --- Preference (economics). --- Price index. --- Principal part. --- Production function. --- Production theory. --- Quasiconvex function. --- Recursive definition. --- Reductio ad absurdum. --- Regular matrix. --- Requirement. --- Row and column vectors. --- Samuelson condition. --- Second derivative. --- Sign (mathematics). --- Special case. --- Statistic. --- Support function. --- Symmetric relation. --- Theorem. --- Theory. --- Transpose. --- Upper and lower bounds. --- Utility. --- Variable (mathematics). --- Welfare economics.
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