The tight groupoid of an inverse semigroup

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• 作者：Ruy Exel ; Enrique Pardo
• 关键词：Inverse semigroup ; Semi ; lattice ; Tight character ; Tight filter ; Ultra ; filter ; Groupoid ; Groupoid C* ; algebra
• 刊名：Semigroup Forum
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：92
• 期：1
• 页码：274-303
• 全文大小：552 KB
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• 作者单位：Ruy Exel (1)
  Enrique Pardo (2)
  
  1. Departamento de Matemática, Universidade Federal de Santa Catarina, Florianópolis, SC, 88010-970, Brazil
  2. Departamento de Matemáticas, Facultad de Ciencias, Universidad de Cádiz, Campus de Puerto Real, 11510, Puerto Real, Cádiz, Spain
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Algebra
  
• 出版者：Springer New York
• ISSN：1432-2137

文摘

In this work we present algebraic conditions on an inverse semigroup \(\mathcal {S}\) (with zero) which imply that its associated tight groupoid \(\mathcal {G}_\mathrm{tight}(\mathcal {S})\) is: Hausdorff, essentially principal, minimal and contracting, respectively. In some cases these conditions are in fact necessary and sufficient. Keywords Inverse semigroup Semi-lattice Tight character Tight filter Ultra-filter Groupoid Groupoid C*-algebra