Potential theory and geometry on Lie groups

by Varopoulos, N.

Type Book

Rate 0.0 /5

Details

Files

Reviews

Download

Title Statements

Full title :Potential theory and geometry on Lie groups / N. Th. Varopoulos.

Summary

"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"--

Edition Statements

Publication Date:©2021

Publication Statements

Publisher(s):Cambridge University Press
Place of Publication:Cambridge, United Kingdom
Language:eng
Publication Date:©2021

The Physical Object

Description:xxvii, 596 pages : : illustrations (black and white) ; : 24 cm.

Edition Identifiers

ISBN:9781107036499, 1107036496
oclc:on1135910200
LC Classification:QA387
Dewey Decimal:512/.482

The classification and the first main theorem -- NC-groups -- The B-NB classification -- NB-Groups -- Other classes of locally compact groups -- The geometric theory. An introduction -- The geometric NC-theorem -- Algebra and geometries on C-groups -- The end game in the C-theorem -- The metric classification -- The homotopy and homology classification of connected Lie groups -- The polynomial homology for simply connected soluble groups -- Cohomology on Lie groups.