Title: Potential Theory and Geometry on Lie Groups (New Mathematical Monographs, Series Number 38)
Publisher: Cambridge University Press
Publication Date: 2020
Language: English
ISBN 10: 1107036496
ISBN 13: 9781107036499
Binding: Hardcover
Condition: New

About this title

Synopsis

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.

About the Author

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

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