Functional Analysis and Its Applications | 2019
On Holomorphic Realizations of Nilpotent Lie Algebras
Abstract
Realizations of five-dimensional Lie algebras as algebras of holomorphic vector fields on homogeneous real hypersurfaces of a three-dimensional complex space are studied. In view of already known results, in the problem of describing such varieties only Levy nondegenerate hypersurfaces with exactly five-dimensional Lie algebras are of interest. It is shown that only two of the nine existing distinct nilpotent Lie algebras admit realizations associated with such varieties, and the varieties corresponding to these exceptional algebras are standard quadrics.