Potential Theory and Geometry on Lie Groups (Hardcover) (ISBN-13: 9781107036499)

This book provides a complete and reasonably self-contained account of a new classification of connected Lie groups into two classes. The first part describes the use of tools from potential theory to establish the classification and to show that the analytic and algebraic approaches to the classification are equivalent. Part II covers geometric theory of the same classification and a proof that it is equivalent to the algebraic approach. Part III is a new approach to the geometric classification that requires more advanced geometric technology, namely homotopy, homology and the theory of currents. Using these methods, a more direct, but also more sophisticated, approach to the equivalence of the geometric and algebraic classification is made. Background material is introduced gradually to familiarise readers with ideas from areas such as Lie groups, differential topology and probability, in particular, random walks on groups. Numerous open problems inspire students to explore further.

Author: N. Th Varopoulos
ISBN-10: 1107036496
ISBN-13: 9781107036499
Publisher: Cambridge University Press
Language: English
Published: 10/22/2020
Pages: 611
Format: Hardcover
Weight: 2.39lbs
Size: 9.00h x 6.00w x 1.50d