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In this paper we denote a type of affine homogeneous real hypersurface of$\mathbb{C}^3$ and present a classification of homogeneous surfaces of the type(1/2,0). The result was obtained by reducing the classification problemmentioned above to the problem of solving a system of nonlinear (quadratic)equations. Solutions of such system represent all the Lie algebrascorresponding to the homogeneous surfaces under consideration. Some details ofintegration procedure are discussed for obtained algebras.

Affine homogeneous strictly pseudoconvex hypersurfaces of the type (1/2,0) in $\mathbb{C}^3$