Isometry from Reflections Versus Isometry from Bivector
Identifieur interne : 000557 ( Main/Merge ); précédent : 000556; suivant : 000558Isometry from Reflections Versus Isometry from Bivector
Auteurs : Zbigniew Oziewicz [Mexique]Source :
- Advances in Applied Clifford Algebras [ 0188-7009 ] ; 2009-12-01.
Abstract
Abstract.: A unipotent isometry is said to be a reflection. In 1937 Élie Cartan proved that every isometry can be expressed as a composition of reflections. The Lie subalgebra of bivectors inside a Clifford algebra generate isometries without the Grassmann exponential. The main result is the coordinate-free and basis-free construction of two isometries from a simple bivector. Hestenes introduced in 1966 a rotor in a Spin group as a square root of the Clifford product of two vectors. We compare a rotor from reflections, with a rotor from a simple bivector. This result generalizes the Lorentz transformations considered by Pertti Lounesto in 1997.
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DOI: 10.1007/s00006-009-0194-z
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