These 14 lectures by a renowned educator focus on applications of continuous groups in geometry and analysis. Their unique perspectives are illustrated by numerous inventive geometric examples. 1971 edition.
These 14 lectures by a renowned educator focus on applications of continuous groups in geometry and analysis. Their unique perspectives are illustrated by numerous inventive geometric examples. 1971 edition.
Charles Loewner was a renowned Professor of Mathematics at Stanford University.
Inhaltsangabe
Preface Lecture I: Transformation Groups Similarity Lecture II: Representations of Groups Combinations of Representations Similarity and Reducibility Lecture III: Representations of Cyclic Groups Representations of Finite Abelian Groups Representations of Finite Groups Lecture IV: Representations of Finite Groups (cont.) Characters Lecture V: Representations of Finite Groups (conc.) Introduction to Differentiable Manifolds Tensor Calculus on a Manifold Lecture VI: Quantities, Vectors, and Tensors Generation of Quantities by Differentiation Commutator of Two Contravariant Vector Fields Hurwitz Integration on a Group Manifold Lecture VII: Hurwitz Integration on a Group Manifold (cont.) Representation of Compact Groups Existence of Representations Lecture VIII: Representation of Compact Groups (cont.) Characters Examples Lecture IX: Lie Groups Infinitesimal Transformations on a Manifold Lecture X: Infinitesimal Transformations of a Group Examples Geometry on the Group Space Lecture XI: Parallelism First Fundamental Theorem of Lie Groups Mayer-Lie Systems Lecture XII: The Sufficiency Proof First Fundamental Theorem Converse Second Fundamental Theorem Converse Lecture XIII: Converse of the Second Fundamental Theorem (cont.) Concept of Group Germ Lecture XIV: Converse of the Third Fundamental Theorem The Helmholtz-Lie Problem Index
Preface Lecture I: Transformation Groups Similarity Lecture II: Representations of Groups Combinations of Representations Similarity and Reducibility Lecture III: Representations of Cyclic Groups Representations of Finite Abelian Groups Representations of Finite Groups Lecture IV: Representations of Finite Groups (cont.) Characters Lecture V: Representations of Finite Groups (conc.) Introduction to Differentiable Manifolds Tensor Calculus on a Manifold Lecture VI: Quantities, Vectors, and Tensors Generation of Quantities by Differentiation Commutator of Two Contravariant Vector Fields Hurwitz Integration on a Group Manifold Lecture VII: Hurwitz Integration on a Group Manifold (cont.) Representation of Compact Groups Existence of Representations Lecture VIII: Representation of Compact Groups (cont.) Characters Examples Lecture IX: Lie Groups Infinitesimal Transformations on a Manifold Lecture X: Infinitesimal Transformations of a Group Examples Geometry on the Group Space Lecture XI: Parallelism First Fundamental Theorem of Lie Groups Mayer-Lie Systems Lecture XII: The Sufficiency Proof First Fundamental Theorem Converse Second Fundamental Theorem Converse Lecture XIII: Converse of the Second Fundamental Theorem (cont.) Concept of Group Germ Lecture XIV: Converse of the Third Fundamental Theorem The Helmholtz-Lie Problem Index
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