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Let $V$ be a $\mathbb{Q}$-Hodge structure and $MT \subset GL_V$ its Mumford-Tate group. Let $I \subset \mathcal{O}_{GL_V}$ be the ideal of functions vanishing on $MT(\mathbb{Q})$.

Is $\mathcal{O}_{GL_V}/I$ equal to the Hopf algebra of $MT$ ?

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    $\begingroup$ The Mumford-Tate group is a connected affine algebraic group. Are there connected affine algebraic groups that do not have this property? $\endgroup$
    – Will Sawin
    Commented Aug 23, 2013 at 17:25
  • $\begingroup$ Not in characteristic zero. $\endgroup$
    – abz
    Commented Aug 24, 2013 at 12:28

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