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<p>This paper focuses on the Benson-Ratcliff invariant in the context of central extensions of nilpotent Lie algebras. We successively analyze the abelian, metabelian and <i>r</i> steps cases, then those of Lie algebras with two-dimensional generic coadjoint orbits. We illustrate this result by explicit computation in the case of 6-dimensional nilpotent Lie algebras with 1-dimensional center and identify all counterexamples to the Benson-Ratcliff conjecture in this class.</p>

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Benson-Ratcliff invariant and central extensions of nilpotent Lie algebras

  • 期刊论文

  • 发表日期：

    2026年5月7日

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  • Rafik Khalfi

摘要

This paper focuses on the Benson-Ratcliff invariant in the context of central extensions of nilpotent Lie algebras. We successively analyze the abelian, metabelian and r steps cases, then those of Lie algebras with two-dimensional generic coadjoint orbits. We illustrate this result by explicit computation in the case of 6-dimensional nilpotent Lie algebras with 1-dimensional center and identify all counterexamples to the Benson-Ratcliff conjecture in this class.