  In this article we characterize the extreme points of the unit ball of a
non-commutative (quantum) Lorentz space associated with a semi-finite von
Neumann algebra. This enables us to show that surjective isometries between
non-commutative Lorentz spaces are projection disjointness preserving and
finiteness preserving, which facilitates a characterization of the structure of
these isometries.
