  The motivation for this paper is to detect when an irreducible projective
variety V is not toric. We do this by analyzing a Lie group and a Lie algebra
associated to V. If the dimension of V is strictly less than the dimension of
the above mentioned objects, then V is not a toric variety. We provide an
algorithm to compute the Lie algebra of an irreducible variety and use it to
provide examples of non-toric statistical models in algebraic statistics.
