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.

翻译：本文的研究动机在于判定不可约射影簇V何时不是环面簇。我们通过分析与V相关联的李群和李代数来实现这一判定。若V的维数严格小于上述对象的维数，则V不是环面簇。我们提出了计算不可约簇李代数的算法，并以此构建了代数统计中非环面统计模型的实例。