Description: 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.
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EAN: 9781107036499
UPC: 9781107036499
ISBN: 9781107036499
MPN: N/A
Book Title: Potential Theory and Geometry on Lie Groups (New M
Number of Pages: 611 Pages
Language: English
Publication Name: Potential Theory and Geometry on Lie Groups
Publisher: Cambridge University Press
Item Height: 1.8 in
Subject: General, Mathematical Analysis
Publication Year: 2020
Type: Textbook
Item Weight: 38.1 Oz
Item Length: 6.3 in
Author: N. Th. Varopoulos
Subject Area: Mathematics
Item Width: 9.3 in
Series: New Mathematical Monographs
Format: Hardcover
