Translation Group

Some articles on translation group, group, translation:

Point Groups In Two Dimensions - Combinations With Translational Symmetry
... E(2) is a semidirect product of O(2) and the translation group T ... In other words O(2) is a subgroup of E(2) isomorphic to the quotient group of E(2) by T O(2) E(2) / T There is a "natural" surjective group homomorphism p E(2) → E(2 ... For every subgroup of E(2) we can consider its image under p a point group consisting of the cosets to which the elements of the subgroup belong, in ...
Glide Plane - Formal Treatment
... space the combination of a reflection in a plane and a translation in that plane ... Depending on context, we may consider a reflection a special case, where the translation vector is the zero vector ... The combination of a reflection in a plane and a translation in a perpendicular direction is a reflection in a parallel plane ...
Glide Reflection
... of isometry of the Euclidean plane the combination of a reflection in a line and a translation along that line ... Depending on context, we may consider a reflection a special case, where the translation vector is the zero vector ... is an isometry consisting of the reflection on the x-axis, followed by translation of one unit parallel to it ...
Teleparallelism - New Translation Teleparallel Gauge Theory of Gravity
... started to formulate the gauge theory of the space-time translation group ... Hayashi pointed out the connection between the gauge theory of space-time translation group and absolute parallelism ... fully represented by the translational gauge potential, as it should be for a gauge theory for the translation group ...

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