Year: 2026
Type: preprint
Abstract: We consider the problem of computing rational invariants of nilpotent Lie algebras. We compare two methods that are commonly used for this task: the method of integral curves and the Dixmier map. Given a derivation of a rational function field with polynomial coefficients, we formulate a condition under which the kernel can be recovered from a family of rational integral curves, and we show that triangular derivations satisfy this hypothesis. This yields an explicit description of the kernel as a purely transcendental extension and produces algebraically independent generators. We also show that, in the triangular case, the resulting generators agree with those obtained from the Dixmier map via a local slice. A careful analysis of the generating set obtained from this method leads to an algorithm for computing generators of the rational invariant field of a nilpotent Lie algebra. An implementation of the methods is available in the SageMath system.
Source: arXiv (Cornell University)
Authors: Schneider, Csaba, Silva, Igor Martins
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212291144