On characterization of Double Danielewski type algebras

Let $k$ be a field. In this paper, we consider Double Danielewski type algebras over an affine factorial $k$-domain $R$. We observe that this family produces a non-cancellative family of algebras over $R$. Further, when $k$ is a field of characteristic zero, we give a characterization for an affine algebra to be isomorphic to an algebra of Double Danielewski type.