Lorentz Group
The Lorentz group is the Group 
of time-preserving linear Isometries of Minkowski Space
with the pseudo-Riemannian metric
It is also the Group of Isometries of 3-D Hyperbolic Space. It is time-preserving in the sensethat the unit time Vector
is sent to another Vector 
such that 
.A consequence of the definition of the Lorentz group is that the full Group of time-preserving isometries ofMinkowski is the Direct Product of the group oftranslations of (i.e., itself, with addition as the group operation), with the Lorentz group, and thatthe full isometry group of the Minkowski is a group extension of 
by theproduct 
.
The Lorentz group is invariant under space rotations and Lorentz Transformations.
See also Lorentz Tensor, Lorentz Transformation
References
Arfken, G. ``Homogeneous Lorentz Group.'' §4.13 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 271-275, 1985.
- Relative Extremum
- Relatively Prime
- Relative Maximum
- Relative Minimum
- Relaxation Methods
- Remainder
- Remainder Theorem
- Rembs' Surfaces
- Removable Crossing
- Removable Singularity
- Rencontres Number
- Rendezvous Values
- Repartition
- Repdigit
- Repeating Decimal
- Repfigit Number
- Replicate
- Representation
- Reptend Prime
- Rep-Tile
- Repunit
- Residual
- Residual vs. Predictor Plot
- Residue Class
- Residue (Complex Analysis)