The Hopf algebra representing the group functor $GL_2$ is the quotient algebra $$ k[X_{00}, X_{01}, X_{10}, X_{11}, t]/((X_{00}X_{11} - X_{01}X_{10})t -1) $$
Consider the $k$-subspace $D(k) \subset GL_2(k)$ generated by $$ \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} $$ as a one dimensional $k$-vector space.
Is there a Hopf Algebra representation for $D$?