Potential Theory and Geometry on Lie Groups

List of contents

Preface; 1. Introduction; Part I. The Analytic and Algebraic Classification: 2. The classification and the first main theorem; 3. NC-groups; 4. The B-NB classification; 5. NB-groups; 6. Other classes of locally compact groups; Appendix A. Semisimple groups and the Iwasawa decomposition; Appendix B. The characterisation of NB-algebras; Appendix C. The structure of NB-groups; Appendix D. Invariant differential operators and their diffusion kernels; Appendix E. Additional results. Alternative proofs and prospects; Part II. The Geometric Theory: 7. The geometric theory. An introduction; 8. The geometric NC-theorem; 9. Algebra and geometries on C-groups; 10. The end game in the C-theorem; 11. The metric classification; Appendix F. Retracts on general NB-groups (not necessarily simply connected); Part III. Homology Theory: 12. The homotopy and homology classification of connected Lie groups; 13. The polynomial homology for simply connected soluble groups; 14. Cohomology on Lie groups; Appendix G. Discrete groups; Epilogue; References; Index.

About the author

N. Th. Varopoulos was for many years a professor at Université de Paris VI. He is a member of the Institut Universitaire de France.

Summary

This book provides a complete and reasonably self-contained account of a new classification of connected Lie groups into two classes. Background material is introduced gradually to familiarise readers with the necessary ideas. A large number of accessible open problems will inspire students to explore further.

Product details

• Authors: N. Th Varopoulos, N. Th. Varopoulos, N. Th. (Universite De Paris VI (Pierre Varopoulos, N. Th. (Universite de Paris VI (Pierre et Marie Curie)) Varopoulos
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Hardback
• Released: 30.06.2020
• EAN: 9781107036499
• ISBN: 978-1-107-03649-9
• No. of pages: 611
• Series: New Mathematical Monographs; New Mathematical Monographs
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra; MATHEMATICS / Algebra / Abstract, Mathematische Analysis, allgemein, MATHEMATICS / Mathematical Analysis, MATHEMATICS / Algebra / General, Mathematics, geometry, Topology, Probability & statistics, Calculus & mathematical analysis, Probability and statistics, Calculus and mathematical analysis