  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.

Quantum Algebra;Algebraic Geometry