On Subalgebras of the Conformal Algebra AC(2,2)

Abstract

Subalgebras of the Lie algebra AC(2, 2) of the group C(2, 2), which is the group of conformal transformations of the pseudo-Euclidean space R _2,2, are studied. All subalgebras of the algebra AC(2, 2) are splitted into three classes, each of those is characterized by the isotropic rank 0, 1, or 3. We present the complete classification of the class 0 subalgebras and also of the class 3 subalgebras which satisfy an additional condition. The results obtained are applied to the reduction problem for the d’Alembert equation □u + λu ³ = 0 in the space R _2,2.