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Potential theory and geometry on Lie groups /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Potential theory and geometry on Lie groups // N. Th. Varopoulos.
作者:	Varopoulos, N.,
面頁冊數:	1 online resource (xxvii, 596 pages) :digital, PDF file(s). :
附註:	Title from publisher's bibliographic system (viewed on 29 Oct 2020).
標題:	Potential theory (Mathematics) -
電子資源:	https://doi.org/10.1017/9781139567718
ISBN:	9781139567718 (ebook)

Potential theory and geometry on Lie groups /
Varopoulos, N.,1940-

Potential theory and geometry on Lie groups /N. Th. Varopoulos. - 1 online resource (xxvii, 596 pages) :digital, PDF file(s). - New mathematical monographs ;38. - New mathematical monographs ;31..

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 (ebook)Subjects--Topical Terms:

672265
Potential theory (Mathematics)

LC Class. No.: QA387 / .V365 2021

Dewey Class. No.: 512/.482

Potential theory and geometry on Lie groups /
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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 Potential theory (Mathematics) $3 672265
650 0 $a Geometry. $3 579899
650 0 $a Lie groups. $3 527929
776 0 8 $i Print version: $z 9781107036499
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