Testing isomorphism of complex Lie algebras
Tuan Anh Nguyen, Vu A. Le, Thieu N. Vo · Communications in Algebra · 2025
This paper studies algorithms for testing isomorphism of Lie algebras over the field of complex numbers. First, we combine the so-called linearization method with effective Nullstellensatz to prove the existence of an algorithm that tests isomorphism of n-dimensional complex Lie algebras using singly-exponential arithmetic operations in n. Second, we construct more practical algorithms for testing isomorphism of complex Lie algebras, including those with parameters, by means of triangular decomposition. Several applications of the proposed algorithms are also discussed.