On Homogeneous CR Manifolds of Arbitrary Order of Levi Nondegeneracy

This paper present homogeneous CR hypersurfaces satisfying the $CR$-invariant property of being $k$-nondegenerate for an arbitrary integer $k\ge 1$. The construction of such homogeneous manifolds are based on $CR$ algebras defined by irreducible representations of $\mathfrak{s}\mathfrak{u}(2)$. An explicit study of the iterated Levi forms with their respective kernels, along with the local model equation, is given.