TY  - GEN
AU  - Varopoulos, N. Th. 
TI  - Potential Theory and Geometry on Lie Groups
T2  - New Mathematical Monographs
SN  - 9781107036499 (HB)
PY  - 2024///
CY  - Cambridge 
PB  - Cambridge University Press
KW  - Lie groups
KW  - Algebraic Groups
KW  - Representation theory
N1  - Includes References (585-588) and Index;     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
N2  - 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.
ER  -