000			02235 a2200241 4500
008			240614b |||||||| |||| 00| 0 eng d
020			_a9781107036499 (HB)
041			_aeng
080			_a512.81 _bVAR
100			_aVaropoulos, N. Th.
245			_aPotential Theory and Geometry on Lie Groups
260			_bCambridge University Press _c2024 _aCambridge
300			_axxvii, 596p.
490			_aNew Mathematical Monographs _v38
504			_aIncludes References (585-588) and Index
505			_a 1. Introduction 2. The classification and the first main theorem 3. NC-groups 4. The B-NB classification 5. NB-Groups 6. Other classes of locally compact groups 7. The geometric theory. An introduction 8. The geometric NC-theorem 9. Algebra and geometries on C-groups 10. The end game in the C-theorem 11. The metric classification 12. The homotopy and homology classification of connected Lie groups 13. The polynomial homology for simply connected soluble groups 14. Cohomology on Lie groups
520			_aThis 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			_aLie groups
650			_aAlgebraic Groups
650			_aRepresentation theory
690			_aMathematics
942			_cBK
999			_c60258 _d60258