Lie Groups, Convex Cones and Semigroups

Joachim Hilgert, etc., Karl H. Hofmann, Jimmie D. Lawson (Autoren)

Buch | Hardcover

683 Seiten

1989
Clarendon Press (Verlag)
978-0-19-853569-0 (ISBN)

Infos

The geometry of convex cones has in recent years come to play an important role in the development of the Lie theory of sub-semigroups of Lie groups. This book attempts to provide an account of this theory and indicates its wide-ranging application to representation theory of Lie groups. In the spirit of classical Lie theory, the authors first develop the infinitesimal theory of Lie sub-semigroups which culminates in a characterization of those cones in a Lie algebra which are invariant under the action of the group of inner automorphisms. The book then discusses the local Lie theory for semigroups before providing an account of the global theory for the existence of sub-semigroups with a given set of infinitesimal generators. Pre-requisites are little more than standard Lie theory and throughout many examples such as the real special linear groups, the Heisenberg group, and Lie groups containing contraction semigroups are discussed in detail.
As a whole, the book should provide an accessible account of this new material and indicates its wide-ranging application to systems theory, geometric control theory, causality on homogeneous spaces, symmetric domains, and the representation theory of Lie groups.

Inhalt

The geometry of cones; wedges in Lie algebras; invariant cones; the local Lie theory of semigroups; subsemigroups of Lie groups; positivity; embedding semigroups into Lie groups.

Produkt-Details

• Erscheint lt. Verlag: 1.11.1989
• Reihe/Serie: Oxford Mathematical Monographs
• Zusatzinfo: line illustrations throughout, bibliography
• Verlagsort: Oxford
• Sprache: englisch
• Maße: 180 x 240 mm
• Gewicht: 1620 g
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• ISBN-10: 0-19-853569-4 / 0198535694
• ISBN-13: 978-0-19-853569-0 / 9780198535690
• Zustand: Neuware