Theory of Continuous Groups

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