Front matter -- Preface -- Acknowledgements -- Table of Contents -- 1. Lie semigroups, ordered symmetric spaces and causality -- Causal semisimple symmetric spaces, the geometry and harmonic analysis / Faraut, Jacques / Ólafsson, Gestur -- The halfspace method for causal structures on homogeneous manifolds / Hilgert, Joachim -- Semigroups in foundations of geometry and axiomatic theory of space-time / Guts, Alexander K. -- On mathematical foundations and physical applications of chronometry / Levichev, Alexander V. -- 2. Invariant cones, Ol'shanskiĭ-semigroups, exponential semigroups -- On the structure of Lie algebras admitting an invariant cone / Gichev, Victor M. -- Semigroups of Ol'shanskiĭ type / Lawson, Jimmie D. -- Lie groups and exponential Lie subsemigroups / Hofmann, Karl H. / Ruppert, Wolfgang A.F. -- 3. Convexity theorems, representation theory -- Symplectic convexity theorems, Lie semigroups, and unitary representations / Hilgert, Joachim / Neeb, Karl-Hermann -- Holomorphic representations of Ol'shanskiĭ semigroups / Neeb, Karl-Hermann -- 4. Semisimple Lie groups and semigroups -- Control sets and semigroups in semisimple Lie groups / Martin, Luiz B. San -- The asymptotic semigroup of a semisimple Lie group / Vinberg, Ernest B. -- 5. Applications: Control -- Applications of the maximum principle to problems in Lie semigroups / Mittenhuber, Dirk -- Totally extremal |