A history of topological and analytical semigroups. A personal view
type: Item
instance of: scholarly article
title: A history of topological and analytical semigroups. A personal view
zbMATH Open document ID: 0952.22001
DOI: 10.1007/PL00006007
published in: Semigroup Forum
publication date: 2001-01-04T00:00:00Z
review text: It does not seem feasible to summarize the author's excellent treatment of the history of topological and analytical semigroups. This reviewer will therefore indicate some of the highlights of the paper and add a small amount of insight of his own. This paper presents a very well conceived historical perspective of the development of topological and analytical semigroups and the researchers that made contributions to this development. The chronology presented at the conclusion of the paper is outstanding. In his 1955 AMS address (referenced in this paper), A. D. Wallace stated that he was reporting on a large number of small theorems, which indicates that topological semigroups theory was in its early stages of discovery. The author points out that an early important discovery of Wallace was the structure of the minimal ideal of a compact semigroup. He also brings to light some of the earlier results of well-known mathematicians that contributed to this and other important facets of the theory. The 1966 AMS address delivered by P. S. Mostert reported on a small number of large theorems, which indicated that substantial depth was being developed in compact semigroup theory. Structure theorems were being discovered by researchers such as Hofmann and Mostert, Koch, Lawson, and their colleagues. D. R. Brown, along with his students and colleagues, later made substantial contributions to the theory of compact divisible semigroups. Through the work of Keimel and others, this theory provided a bridge to Lie semigroup theory. In more recent times (as indicated by the author), the frontier of Lie semigroup theory has been extended. The primary contributors here are Hofmann, Lawson, and their colleagues.
Mathematics Subject Classification ID: 22-03
Mathematics Subject Classification ID: 01A65
zbMATH DE Number: 1491097
zbMATH Keywords: topological semigroup
zbMATH Keywords: analytical semigroup
zbMATH Keywords: Lie semigroup
zbMATH Keywords: completely simple semigroup
zbMATH Keywords: bicyclic semigroup
zbMATH Keywords: divisible semigroup
zbMATH Keywords: compact semigroup
zbMATH Keywords: group
zbMATH Keywords: monoid
zbMATH Keywords: semilattice
zbMATH Keywords: semialgebra
zbMATH Keywords: lambda calculus
zbMATH Keywords: acyclic
zbMATH Keywords: cone
zbMATH Keywords: wedge
zbMATH Keywords: centralizer
author: Karl H. Hofmann
reviewed by: John A. Hildebrant
MaRDI profile type: Publication
full work available at URL: pl00006007
OpenAlex ID: W2067881858
description: scientific article; zbMATH DE number 1491097