: U.S. ISBN 9780387962405
This book is intended as an introductory text on the subject of Lie groups and algebras and their role in various fields of mathematics and physics. It is written by and for researchers who are primarily analysts or physicists, not algebraists or geometers. Not that we have eschewed the algebraic and geo- metric developments. But we wanted to present them in a concrete way and to show how the subject interacted with physics, geometry, and mechanics. These interactions are, of course, manifold; we have discussed many of them here-in particular, Riemannian geometry, elementary particle physics, sym- metries of differential equations, completely integrable Hamiltonian systems, and spontaneous symmetry breaking. Much ofthe material we have treated is standard and widely available; but we have tried to steer a course between the descriptive approach such as found in Gilmore and Wybourne, and the abstract mathematical approach of Helgason or Jacobson. Gilmore and Wybourne address themselves to the physics community whereas Helgason and Jacobson address themselves to the mathematical community. This book is an attempt to synthesize the two points of view and address both audiences simultaneously. We wanted to present the subject in a way which is at once intuitive, geometric, applications- oriented, mathematically rigorous, and accessible to students and researchers without an extensive background in physics, algebra, or geometry.
A Lie Groups and Algebras.- 1 Lie Groups.- 2 Lie Algebras.- 3 Lie Groups and Algebras: Matrix Approach.- 4 Applications to Physics and Vice Versa.- B Differential Geometry and Lie Groups.- 5 Calculus on Manifolds.- 6 Symmetry Groups of Differential Equations.- 7 Invariant Forms on Lie Groups.- 8 Lie Groups and Algebras: Differential Geometric Approach.- C Algebraic Theory.- 9 General Structure of Lie Algebras.- 10 Structure of Semi-Simple Lie Algebras.- 11 Real Forms.- D Representation Theory.- 12 Representation Theory.- 13 Spinor Representations.- E Applications.- 14 Applications.
: Germany ISBN 9783540962403
This is an introductory text on Lie groups and algebras and their roles in diverse areas of pure and applied mathematics and physics. The material is presented in a way that is at once intuitive, geometric, applications oriented, and, most of the time, mathematically rigorous. It is intended for students and researchers without an extensive background in physics, algebra, or geometry. In addition to an exposition of the fundamental machinery of the subject, there are many concrete examples that illustrate the role of Lie groups and algebras in various fields of mathematics and physics: elementary particle physics, Riemannian geometry, symmetries of differential equations, completely integrable systems, and bifurcation theory.
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