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Lie Semigroups and their Applications
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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 associatedOl'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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