Potential Theory and Geometry on Lie Groups
(Part of the New Mathematical Monographs Series)
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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.
Format:Hardcover
Language:English
ISBN:1107036496
ISBN13:9781107036499
Release Date:October 2020
Publisher:Cambridge University Press
Length:611 Pages
Weight:2.39 lbs.
Dimensions:1.5" x 6.0" x 9.0"
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