GL (4.C) in
terms of 16 basic elements of the Dirac matrix algebra.
Alternatively to the use of 16 tensor quantities, the possibility
to parameterize the group GL(4.C) with the help of four
4-dimensional complex vectors (k, m, n, l) is investigated.
The multiplication rules G'G are formulated in the form of a
bilinear function of two sets of 16 variables. The detailed
investigation is restricted to 6-parameter case G(A,B,Fkl),
which provides us with spinor covering for the complex
orthogonal group SO(3,1.C). The complex Euler's angles
parametrization for the last group is also given. Many different
parameterizations of the group based on the curvilinear
coordinates for complex extension of the 3-space of constant
curvature are discussed. The use of the Newmann-Penrose formalism
and applying quaternion techniques in the theory of complex
Lorentz group are considered. Connections between Einstein-Mayer
study on semi-vectors and Fedorov's treatment of the Lorentz group
theory are stated in detail. Classification of fermions in
intrinsic parities is given on the base of the theory of
representations for spinor covering of the complex Lorentz group.
Key words: Dirac matrices, orthogonal groups, covering group, discrete transformations, intrinsic parity, fermion, semi-vectors, Newmann-Penrose formalism, Majorana basis
