ALMOST ABELIAN LIE GROUPS, SUBGROUPS AND QUOTIENTS

An almost Abelian Lie group is a non-Abelian with codimension 1 normal subgroup. The majority of 3-dimensional real groups are Abelian, and they appear in all parts physics that deal anisotropic media—cosmology, crystallography etc. In theoretical differential geometry, their homogeneous spaces provide some the simplest solvmanifolds on which variety geometric structures, such as symplectic, Kähler, spin etc., currently studied explicit terms. Recently, algebras were classified details. However, systematic investigation has not been carried out yet, present paper devoted to an description properties this wide diverse class groups. subject aspects, exponential map, faithful matrix representations, discrete connected subgroups, quotients automorphisms. emphasis put technical