An Algorithm for Determining Lie Algebra Types

2025/12/04 by Tan N. Nguyen, Nguyen, Tu N. T. C., Tuan A. Nguyen +3
Computer Science · Mathematics · #15A21 #17B05 #68W30 #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Polynomial and algebraic computation #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2512.04438

openalex publication_date 2025/12/04 · openalex created_date 2025/12/06 · openalex updated_date 2026/07/28

Abstract

This paper investigates the Jordan--Kronecker invariant of finite dimensional complex Lie algebras. We present an explicit algorithm for determining the type of a given Lie algebra from its Jordan--Kronecker invariant. The algorithm is implemented in a specific Matlab program.

Citations

• Classification of 7-dimensional solvable Lie algebras having 5-dimensional nilradicals
• Jordan-Kronecker invariants of finite-dimensional Lie algebras

Related

• Jordan-Kronecker invariants of finite-dimensional Lie algebras
• New techniques for calculation of Jordan-Kronecker invariants for Lie algebras and Lie algebra representations
• Jordan-Kronecker invariants of Lie algebra representations and degrees of invariant polynomials
• Jordan-Kronecker invariants of Lie algebra representations: examples and computations
• Realization of Jordan-Kronecker invariants by Lie algebras