Memoirs of the American Mathematical Society 1993; 193 pp; softcover Volume: 104 ISBN10: 0821825623 ISBN13: 9780821825624 List Price: US$42 Individual Members: US$25.20 Institutional Members: US$33.60 Order Code: MEMO/104/499
 This work presents the first systematic treatment of invariant Lie semigroups. Because these semigroups provide interesting models for spacetimes in general relativity, this work will be useful to both mathematicians and physicists. It will also appeal to engineers interested in biinvariant control systems on Lie groups. Neeb investigates closed invariant subsemigroups of Lie groups which are generated by oneparameter semigroups and the sets of infinitesimal generators of such semigroupsinvariant convex cones in Lie algebras. In addition, a characterization of those finitedimensional real Lie algebras containing such cones is obtained. The global part of the theory deals with globality problems (Lie's third theorem for semigroups), controllability problems, and the facial structure of Lie semigroups. Neeb also determines the structure of the universal compactification of an invariant Lie semigroup and shows that the lattice of idempotents is isomorphic to a lattice of faces of the cone dual to the cone of infinitesimal generators. Readership Mathematicians interested in the geometry of cones, semigroups, and their compactifications. Table of Contents  Introduction
 Invariant cones in \(K\)modules
 Lie algebras with cone potential
 Invariant cones in Lie algebras
 Faces of Lie semigroups
 Compactifications of subsemigroups of locally compact groups
 Invariant subsemigroups of Lie groups
 Controllability of invariant wedges
 Globality of invariant wedges
 Bohr compactifications
 The unit group of \(S^\flat\)
 Faces and idempotents
 Examples and special cases
 References
