The Nodal Cubic is a Quantum Homogeneous Space
  The cusp was recently shown to admit the structure of a quantum homogeneous space, that is, its coordinate ring $B$ can be embedded as a right coideal subalgebra into a Hopf algebra $A$ such that $A$ is faithfully flat as a $B$-module. In the present article such a Hopf algebra $A$ is constructed for the coordinate ring $B$ of the nodal cubic, thus further motivating the question which affine varieties are quantum homogeneous spaces. 
Ulrich Kraehmer and Angela Tabiri
math.QA math.AG