Toric Structure in Statistical Models through Symmetry Lie Algebra
Published in arXiv.org, 2023
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.