Electronic ISBN:  9781470400767 
Product Code:  MEMO/104/499.E 
List Price:  $45.00 
MAA Member Price:  $40.50 
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 104; 1993; 193 ppMSC: Primary 22; 43;
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 semigroups—invariant 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.
ReadershipMathematicians interested in the geometry of cones, semigroups, and their compactifications.

Table of Contents

Chapters

Introduction

I. Invariant cones in $K$modules

II. Lie algebras with cone potential

III. Invariant cones in Lie algebras

IV. Faces of Lie semigroups

V. Compactifications of subsemigroups of locally compact groups

VI. Invariant subsemigroups of Lie groups

VII. Controllability of invariant wedges

VIII. Globality of invariant wedges

IX. Bohr compactifications

X. The unit group of $S^\flat $

XI. Faces and idempotents

XII. Examples and special cases


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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 semigroups—invariant 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.
Mathematicians interested in the geometry of cones, semigroups, and their compactifications.

Chapters

Introduction

I. Invariant cones in $K$modules

II. Lie algebras with cone potential

III. Invariant cones in Lie algebras

IV. Faces of Lie semigroups

V. Compactifications of subsemigroups of locally compact groups

VI. Invariant subsemigroups of Lie groups

VII. Controllability of invariant wedges

VIII. Globality of invariant wedges

IX. Bohr compactifications

X. The unit group of $S^\flat $

XI. Faces and idempotents

XII. Examples and special cases