Subsemigroups of finite-dimensional Lie groups that are generated
by one-parameter semigroups are the subject of this book. It covers
basic Lie theory for such semigroups and some closely related
topics. These include ordered homogeneous manifolds, where the
order is defined by a field of cones, invariant cones in Lie
algebras and associated Ol'shanskii semigroups. Applications to
representation theory, symplectic geometry and Hardy spaces are
also given. The book is written as an efficient guide for those
interested in subsemigroups of Lie groups and their applications in
various fields of mathematics (see the User's guide at the end of
the Introduction). Since it is essentially self-contained and leads
directly to the core of the theory, the first part of the book can
also serve as an introduction to the subject. The reader is merely
expected to be familiar with the basic theory of Lie groups and Lie
algebras.
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