More on cancellative semigroups on manifolds
type: Item
instance of: scholarly article
title: More on cancellative semigroups on manifolds
zbMATH Open document ID: 0635.22003
DOI: 10.1007/BF02573126
author: B. George
published in: Semigroup Forum
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/134917
review text: The paper deals with cancellative topological semigroups which, as topological spaces, are connected, paracompact, finite dimensional and locally Euclidean. \textit{D. R. Brown} and \textit{R. S. Houston} [Semigroup Forum 35, 279-302 (1987; Zbl 0626.22001)] proved that such a semigroup S can be locally embedded into a simply connected Lie group G(S). This embedding is achieved by constructing local groups of one sided quotients. In the same paper Brown and Houston use the explicit construction of this embedding to provide the semigroup with an analytic structure and give some functorial properties of the semigroups in question. The present paper shows how to obtain the analytic structure of the semigroup and various functorial properties using only the topological and algebraic properties of the Brown-Houston local embedding. The main step is to equip the direct product \(S\times G(S)\) with a topology for which both projections, \(S\times G(S)\to S\) and \(S\times G(S)\to G(S)\) are Hausdorff sheaves of topological spaces. From these sheaves various invariants are constructed which, in the future, may be helpful in deciding whether S can be embedded globally into G(S).
reviewed by: Joachim Hilgert
Mathematics Subject Classification ID: 22A15
Mathematics Subject Classification ID: 22E05
zbMATH DE Number: 4034020
zbMATH Keywords: cancellative topological semigroups
zbMATH Keywords: simply connected Lie group
zbMATH Keywords: local groups
zbMATH Keywords: analytic structure
zbMATH Keywords: local embedding
zbMATH Keywords: Hausdorff sheaves of topological spaces
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4034020