Invariant subsemigroups of Lie groups / Karl-Hermann Neeb.

Format:

Book

Author/Creator:

Neeb, Karl-Hermann, author.

Series:

Memoirs of the American Mathematical Society ; Volume 104, Number 499.

Memoirs of the American Mathematical Society, 0065-9266 ; Volume 104, Number 499

Language:

English

Subjects (All):

Lie algebras.

Lie groups.

Semigroups.

Physical Description:

1 online resource (209 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 1993.

Language Note:

English

Summary:

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 investigates closed invariant subsemigroups of Lie groups which are generated by one-parameter semigroups and the sets of infinitesimal generators of such semigroups---invariant convex cones in Lie algebras. In addition, a characterization of those finite-dimensional 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.

Contents:

""Table of Contents""; ""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. ControllabiKty of Invariant Wedges""; ""VIII. Globality of Invariant Wedges""; ""IX. Bohr Compactifications""; ""X. The Unit Group of S[sup(b)]""; ""XI. Faces and Idempotents""; ""XII. Examples and Special Cases""; ""References""

Notes:

"July 1993, Volume 104, number 499 (end of volume)."

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-0076-6