On Inductive Limit Type Actions of the Euclidean Motion Group on Stable UHF Algebras

2006 ◽  
Vol 49 (2) ◽  
pp. 213-225
Author(s):  
Andrew J. Dean
Keyword(s):  
Dynamical Systems ◽  
Inductive Limit ◽  
Unitary Representations ◽  
Motion Group ◽  
Direct Sums ◽  
Euclidean Motion Group ◽  
Euclidean Motion

AbstractAn invariant is presented which classifies, up to equivariant isomorphism, C*-dynamical systems arising as limits from inductive systems of elementary C*-algebras on which the Euclidean motion group acts by way of unitary representations that decompose into finite direct sums of irreducibles.

scholarly journals Applications of the Exponential Function of the Euclidean Motion Group to the Theory of Gearing

2014 ◽  
Vol 6 ◽  
pp. 869580
Author(s):  
Baozhen Lei ◽  
Harald Löwe ◽  
Xunwei Wang
Keyword(s):  
Differential Geometry ◽  
Exponential Function ◽  
Machine Tools ◽  
Basic Equation ◽  
Time Parameter ◽  
Motion Group ◽  
New Approach ◽  
Euclidean Motion Group ◽  
Special Machine ◽  
Euclidean Motion

The present paper provides a first step to a new approach to the theory of gearing, which uses modern differential geometry in order to ensure a strict and coordinate-independent formulation. Here, we are mainly concerned with a basic equation, namely, the equation of meshing, of two rotating surfaces in mesh. Since we are able to solve this equation by the time parameter, we derive parameterizations of the mating pinion from a bevel gear as well as a parameterization for gears produced by special machine tools.

scholarly journals On theorems of Beurling and Hardy for the Euclidean Motion group

2005 ◽  
Vol 57 (3) ◽  
pp. 335-351 ◽  
Author(s):  
Rudra P. Sarkar ◽  
Sundaram Thangavelu
Keyword(s):  
Motion Group ◽  
Euclidean Motion Group ◽  
Euclidean Motion

Variants of stability of discontinuous groups for Euclidean motion groups

2017 ◽  
Vol 28 (06) ◽  
pp. 1750046 ◽  
Author(s):  
Ali Baklouti ◽  
Souhail Bejar
Keyword(s):  
Lie Group ◽  
Closed Subgroup ◽  
Deformation Parameter ◽  
Motion Group ◽  
Discontinuous Group ◽  
Euclidean Motion Group ◽  
Euclidean Motion ◽  
Motion Groups ◽  
Discontinuous Groups ◽  
Properly Discontinuous Action

Let [Formula: see text] be a Lie group, [Formula: see text] a closed subgroup of [Formula: see text] and [Formula: see text] a discontinuous group for the homogeneous space [Formula: see text]. Given a deformation parameter [Formula: see text], the deformed subgroup [Formula: see text] may fail to act properly discontinuously on [Formula: see text]. To understand this phenomenon in the case when [Formula: see text] stands for an Euclidean motion group [Formula: see text], we compare the notion of stability for discontinuous groups (cf. [T. Kobayashi and S. Nasrin, Deformation of properly discontinuous action of [Formula: see text] on [Formula: see text], Int. J. Math. 17 (2006) 1175–1193]) with its variants. We prove that the defined stability variants hold when [Formula: see text] turns out to be a crystallographic subgroup of [Formula: see text].

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