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Carnot groups are specific examples of Carnot-Carathéodory spaces. They are simply connected nilpotent Lie groups whose Lie algebras admit particular gradings: stratifications. The polarizations correspond to the first layers of stratifications with norms on them. Every such sub-Finsler Lie group is self-similar with respect to its Carnot-Carathéodory metric. Specifically, there is a natural family of metric dilations.

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Carnot Groups

  • 章节

  • 出版模式：

    开放获取

  • 发表日期：

    2025年

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  • Enrico Le Donne

摘要

Carnot groups are specific examples of Carnot-Carathéodory spaces. They are simply connected nilpotent Lie groups whose Lie algebras admit particular gradings: stratifications. The polarizations correspond to the first layers of stratifications with norms on them. Every such sub-Finsler Lie group is self-similar with respect to its Carnot-Carathéodory metric. Specifically, there is a natural family of metric dilations.