Euclidean group

Target entity: Euclidean group
Context triple: [Euclidean space, hasSymmetryGroup, Euclidean group]

• A. Poincaré group
  The Poincaré group is the fundamental symmetry group of special relativity, combining spacetime translations with Lorentz transformations in four-dimensional Minkowski space.
• B. Lorentz group
  The Lorentz group is the mathematical group of spacetime symmetries in special relativity, consisting of all rotations and boosts that preserve the Minkowski spacetime interval.
• C. Euclidean space
  Euclidean space is the standard flat, n-dimensional geometric setting of classical geometry and vector calculus, characterized by straight lines, right angles, and the usual distance and dot product.
• D. Erlangen Program
  The Erlangen Program is Felix Klein’s influential 1872 framework that classifies and studies geometries based on their underlying symmetry groups and transformation properties.
• E. Weyl group
  A Weyl group is a finite reflection group associated with a root system that encodes the symmetries of Lie algebras and Lie groups in representation theory and geometry.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Euclidean group
Target entity description: The Euclidean group is the group of all distance-preserving transformations of Euclidean space, consisting of rotations, reflections, and translations.

• A. Poincaré group
  The Poincaré group is the fundamental symmetry group of special relativity, combining spacetime translations with Lorentz transformations in four-dimensional Minkowski space.
• B. Lorentz group
  The Lorentz group is the mathematical group of spacetime symmetries in special relativity, consisting of all rotations and boosts that preserve the Minkowski spacetime interval.
• C. Euclidean space
  Euclidean space is the standard flat, n-dimensional geometric setting of classical geometry and vector calculus, characterized by straight lines, right angles, and the usual distance and dot product.
• D. Erlangen Program
  The Erlangen Program is Felix Klein’s influential 1872 framework that classifies and studies geometries based on their underlying symmetry groups and transformation properties.
• E. Weyl group
  A Weyl group is a finite reflection group associated with a root system that encodes the symmetries of Lie algebras and Lie groups in representation theory and geometry.
• F. None of above. chosen