Semigroups in Möbius and Lorentzian Geometry

被引：0

作者：

Jimmie D. Lawson

机构：

[1] Louisiana State University,Department of Mathematics

来源：

Geometriae Dedicata | 1998年 / 70卷

关键词：

Mobius geometry; Lorenz group; Lie semigroups;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

The Möbius semigroup studied in this paper arises very naturally geometrically as the (compression) subsemigroup of the group of Möbius transformations which carry some fixed open Möbius ball into itself. It is shown, using geometric arguments, that this semigroup is a maximal subsemigroup. A detailed analysis of the semigroup is carried out via the Lorentz representation, in which the semigroup resurfaces as the semigroup carrying a fixed half of a Lorentzian cone into itself. Close ties with the Lie theory of semigroups are established by showing that the semigroup in question admits the structure of an Ol'shanskii semigroup, the most widely studied class of Lie semigroups.

引用

页码：139 / 180

页数：41

共 19 条

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