Infinite-dimensional Lie Groups

General Theory and Main Examples
2018
ISBN: 978-0-387-09444-1
Verlag: Springer

Buch, Englisch, 350 Seiten, Format (B × H): 155 mm x 235 mm

provides a comprehensive introduction to this important subject by developing a global infinite-dimensional Lie theory on the basis that a Lie group is simply a manifold modeled on a locally convex space, equipped with a group structure with smooth group operations. The focus is on the local and global level, as well as on the translation mechanisms allowing or preventing passage between Lie groups and Lie algebras. Starting from scratch, the reader is led from the basics of the theory through to the frontiers of current research.

This introductory volume subtitled, , examines the structure theory of infinite-dimensional Lie groups by developing a broad framework of Lie theory and illustrating the general results through a detailed discussion of the major classes of Lie groups. Together with its companion volume subtitled, , these essentially self-containedtexts provide all necessary background as regards generally locally convex spaces, finite-dimensional Lie theory and differential geometry, with modest prerequisites limited to a basic knowledge of abstract algebra, point set topology, differentiable manifolds, and functional analysis in Banach spaces. The clear exposition includes careful explanations, illustrative examples, numerous exercises, and detailed cross-references to simplify a non-linear reading of the material.

Zielgruppe

Research

Autoren/Hrsg.

Glöckner, Helge

Neeb, Karl-Hermann

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

Preface.- Introduction.- Infinite-dimensional Calculus.- Infinite-dimensional Manifolds.- Lie Groups.- Locally Exponential Lie Groups.- Linear Lie Groups.- Direct Limits of Lie Groups.- Groups of Maps.- Groups of Diffeomorphisms.- Appendix A: Tools from Topology.- Appendix B: Basic Theory of Locally Convex Spaces.- Appendix C: Finite-dimensional Lie Algebras.- Appendix D: Calculus in Banach Spaces.- Appendix E: Smooth Maps into non-Lie Groups.- Appendix F: Cohomology of Lie Algebras.- Bibliography.- Index.