Description
Springer Lie Semigroups and their Applications by Joachim Hilgert, Karl-Hermann Neeb
Subsemigroups of finite-dimensional Lie groups that are_x000D_generated by one-parameter semigroups are the subject of_x000D_this book. It covers basic Lie theory for such semigroups_x000D_and some closely related topics. These include ordered_x000D_homogeneous manifolds, where the order is defined by a field_x000D_of cones, invariant cones in Lie algebras and associated_x000D_Ol'shanskii semigroups. Applications to representation_x000D_theory, symplectic geometry and Hardy spaces are also given._x000D_The book is written as an efficient guide for those_x000D_interested in subsemigroups of Lie groups and their_x000D_applications in various fields of mathematics (see the_x000D_User's guide at the end of the Introduction). Since it is_x000D_essentially self-contained and leads directly to the core of_x000D_the theory, the first part of the book can also serve as an_x000D_introduction to the subject._x000D_The reader is merely expected to be familiar with the basic_x000D_theory of Lie groups and Lie algebras._x000D_ Table of contents :- _x000D_
Lie semigroups and their tangent wedges.- Examples.- Geometry and topology of Lie semigroups.- Ordered homogeneous spaces.- Applications of ordered spaces to Lie semigroups.- Maximal semigroups in groups with cocompact radical.- Invariant Cones and Ol'shanskii semigroups.- Compression semigroups.- Representation theory.- The theory for Sl(2)._x000D_