کتاب دانلود کتب لاتین علوم مهندسیریاضی
نظریه و هندسه بالقوه در گروه های لای
نظریه و هندسه بالقوه در گروه های لای

Potential Theory and Geometry on Lie Groups
نویسنده: N. Th. Varopoulos
سال انتشار: 2021
تعداد صفحات: 625
زبان فایل: English
فرمت فایل: pdf
حجم فایل: 5MB

دانلود رایگان

Publisher : Cambridge University Press

ISBN-10 : 1107036496

ISBN-13 : 978-1107036499

ASIN : B0868Q7BT2

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.