## 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 sense that 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 of Minkowski is the Direct Product of the group of translations of (i.e., itself, with addition as the group operation), with the Lorentz group, and that the full isometry group of the Minkowski is a group extension of by the product .

The Lorentz group is invariant under space rotations and Lorentz Transformations.

References

Arfken, G. Homogeneous Lorentz Group.'' §4.13 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 271-275, 1985.