Linear dilatation structures and inverse semigroups

2007/05/28 by Marius Buliga, Buliga, Marius
Mathematics · #20F65 #20M18 #22E20 #FOS: Mathematics #Group Theory (math.GR) #Metric Geometry (math.MG) #math.GR #math.MG #msc:20F65 #msc:20M18 #msc:22E20

paper · pdf · doi:10.48550/arxiv.0705.4009

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arxiv created 2007/06/07 · arxiv updated 2009/12/01

Abstract

Here we prove that for dilatation structures linearity (see arXiv:0705.1440v1) is equivalent to a statement about the inverse semigroup generated by the family of dilatations of the space. The result is new for Carnot groups and the proof seems to be new even for vector spaces.

Citations

• Contractible groups and linear dilatation structures

Related

• Contractible groups and linear dilatation structures
• Dilation theorems for contractive semigroups
• Dilatation structures II. Linearity, self-similarity and the Cantor set
• Introduction to inverse semigroups
• Regular Dilation and Nica-covariant Representation on Right LCM Semigroups