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<p>Inspired by the celebrated work of Rothschild and Stein, we investigate explicit liftings of some smooth vector fields satisfying the bracket-generating condition with step depending on the point, to Lie algebras. The examples we focus on are certain decoupled domains introduced by Nagel and Stein, whose boundaries provide a natural setting for such constructions. We present explicit models for the lifted Lie algebras associated with these boundaries and analyze their structural properties.</p>

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Lifting Lie algebra on certain decoupled boundaries

  • 期刊论文

  • 发表日期：

    2026年1月3日

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  • Der-Chen Chang,
  • Ji Li,
  • Alessandro Ottazzi,
  • Liangchuan Wu

摘要

Inspired by the celebrated work of Rothschild and Stein, we investigate explicit liftings of some smooth vector fields satisfying the bracket-generating condition with step depending on the point, to Lie algebras. The examples we focus on are certain decoupled domains introduced by Nagel and Stein, whose boundaries provide a natural setting for such constructions. We present explicit models for the lifted Lie algebras associated with these boundaries and analyze their structural properties.