Symmetry Lie Algebras of Varieties with Applications to Algebraic Statistics
Abstract
Abstract. The motivation for this paper is to detect when an irreducible projective variety [Formula: see text] is not toric. This is achieved by analyzing a Lie group and a Lie algebra associated with [Formula: see text]. If the dimension of [Formula: see text] is strictly less than the dimension of the aforementioned objects, then [Formula: see text] is not a toric variety. We provide an algorithm to compute the Lie algebra of an irreducible variety and use it to present examples of nontoric statistical models in algebraic statistics.
Fields of Study & Subjects
Advanced Topics in Algebra
Advanced Algebra and Geometry
Nonlinear Waves and Solitons
Publication details
- Journal / source
- SIAM Journal on Applied Algebra and Geometry
- Publisher
- Society for Industrial & Applied Mathematics (SIAM)
- Volume
- 10
- Issue
- 1
- Pages
- 133–152
- Publication date
- 5 March 2026
- Language
- EN