Subgroups of the group of generalized Lorentz transformations and their geometric invariants

Abstract:
Finite transformations belonging to two noncompact subgroups of the group of generalized Lorentz transformations are found in an explicit form. The group of generalized Lorentz transformations is the linear group, which leaves invariant the metric of a flat Finslerian event space with a partially broken 3D isotropy as well as the corresponding nonlinear generalized Dirac equation. The above-mentioned subgroups play a key role in constructing exact solutions of such an equation.