Tian-Todorov theorem on the deformation of CR-structures on Lie algebras

In this paper, we introduce the Tian-Todorov theorem concerning deformations of CR (Cauchy-Riemann)-structures on Lie algebras. We obtain some conclusions about the smoothing of Kuranishi spaces on Lie algebras with respect to the deformation of CR-structures, i.e., under the assumptions that the constants of the CR-structures are zero, the cohomology groups of operators d^primeand d^prime primeare equal and that the differential operator d can be decomposed into the sum of d^primeand d^prime prime it can be concluded that the deformation of CR-structures on Lie algebras is unobstructed (see Theorem <xref specific-use="ref">main-thm</xref>).