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Potential theory and geometry on Lie groups

Record Type:	Electronic resources : Monograph/item
Title/Author:	Potential theory and geometry on Lie groupsN. Th. Varopoulos.
Author:	Varopoulos, N.
Published:	Cambridge :Cambridge University Press,2021.
Description:	xxvii, 596 p. :ill., digital ;24 cm.
Notes:	Title from publisher's bibliographic system (viewed on 29 Oct 2020).
Subject:	Lie groups.
Online resource:	https://doi.org/10.1017/9781139567718
ISBN:	9781139567718$q(electronic bk.)

Potential theory and geometry on Lie groups
Varopoulos, N.

Potential theory and geometry on Lie groups[electronic resource] /N. Th. Varopoulos. - Cambridge :Cambridge University Press,2021. - xxvii, 596 p. :ill., digital ;24 cm. - New mathematical monographs ;38. - New mathematical monographs ;30..

Title from publisher's bibliographic system (viewed on 29 Oct 2020).

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.

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.

ISBN: 9781139567718$q(electronic bk.)Subjects--Topical Terms:

190898
Lie groups.

LC Class. No.: QA387 / .V365 2021

Dewey Class. No.: 512.482

Potential theory and geometry on Lie groups
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100 1 $a Varopoulos, N. $3 930269
245 1 0 $a Potential theory and geometry on Lie groups $h [electronic resource] / $c N. Th. Varopoulos.
260 $a Cambridge : $b Cambridge University Press, $c 2021.
300 $a xxvii, 596 p. : $b ill., digital ; $c 24 cm.
490 1 $a New mathematical monographs ; $v 38
500 $a Title from publisher's bibliographic system (viewed on 29 Oct 2020).
505 0 $a 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.
520 $a 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.
650 0 $a Lie groups. $3 190898
650 0 $a Geometry. $3 183883
650 0 $a Potential theory (Mathematics) $3 205715
830 0 $a New mathematical monographs ; $v 30. $3 767212
856 4 0 $u https://doi.org/10.1017/9781139567718