無限次元リー群 Infinite-Dimensional Lie Groups : General Theory and Main Examples (Graduate Texts in Mathematics)

Glockner, Helge/ Neeb, Karl-Hermann

Springer Verlag（2012/11発売）

• 製本 Hardcover:ハードカバー版／ページ数 350 p.
• 言語 ENG
• 商品コード 9780387094441
• DDC分類 512

Full Description

Provides a comprehensive introduction to this important subject, examining the basic structure theory of infinite-dimensional Lie groups Essentially self-contained, provides all necessary background, excepting modest prerequisites Clear exposition includes careful explanations, illustrative examples, numerous exercises, and detailed cross-references to simplify a non-linear reading of the material

Contents

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.