Complex Lorentz Group with a Real Metric: Group Structure

In the attempts to connect the Lorentz group and the internal symmetry group of fundamental particles, a 16-parameter connected, noncompact group of rank 4 is studied in detail. The subgroup structure, Lie algebra and its complex extension (which is $A_3$ in Cartan's notation),little groups, the inhomogeneous groups, and the group invariants are discussed.