Lectures on Advanced Mathematical Methods for Physicists

Abstract

Part I:Topology Homotopy Differentiable Manifolds I Differentiable Manifolds II (Riemannian Manifolds), Homology and Cohomology Fibre Bundles Part II:Review of Groups and Related Structures Review of Group Representations Lie Groups and Lie Algebras Linear Representations of Lie Algebras Complexification and Classification of Lie Algebras Geometry of Roots for Compact Simple Lie Algebras Positive Roots, Simple Roots, Dynkin Diagrams Lie Algebras and Dynkin Diagrams for SO(2I), SO(2I+1), USp(2I), SU(I+1) Complete Classification of All CSLA Simple Root Systems Representations of Compact Simple Lie Algebras, Spinor Representations for Real Orthogonal and Pseudo-Orthogonal Groups