By D.H. Sattinger, O.L. Weaver
This ebook is meant as an introductory textual content near to Lie teams and algebras and their function in numerous fields of arithmetic and physics. it's written via and for researchers who're essentially analysts or physicists, no longer algebraists or geometers. no longer that we've got eschewed the algebraic and geo metric advancements. yet we needed to provide them in a concrete means and to teach how the topic interacted with physics, geometry, and mechanics. those interactions are, after all, manifold; we've mentioned lots of them here-in specific, Riemannian geometry, uncomplicated particle physics, sym metries of differential equations, thoroughly integrable Hamiltonian platforms, and spontaneous symmetry breaking. a lot ofthe fabric we now have handled is average and broadly on hand; yet we've got attempted to guide a path among the descriptive strategy akin to present in Gilmore and Wybourne, and the summary mathematical method of Helgason or Jacobson. Gilmore and Wybourne tackle themselves to the physics group while Helgason and Jacobson tackle themselves to the mathematical neighborhood. This ebook is an try to synthesize the 2 issues of view and deal with either audiences concurrently. we needed to provide the topic in a fashion that is instantly intuitive, geometric, functions orientated, mathematically rigorous, and available to scholars and researchers with out an in depth heritage in physics, algebra, or geometry.