Corpus ID: 227210349

Polynomial and horizontally polynomial functions on Lie groups

@article{Antonelli2020PolynomialAH,
  title={Polynomial and horizontally polynomial functions on Lie groups},
  author={Gioacchino Antonelli and Enrico Le Donne},
  journal={arXiv: Group Theory},
  year={2020}
}
We generalize both the notion of polynomial functions on Lie groups and the notion of horizontally affine maps on Carnot groups. We fix a subset $S$ of the algebra $\mathfrak g$ of left-invariant vector fields on a Lie group $\mathbb G$ and we assume that $S$ Lie generates $\mathfrak g$. We say that a function $f:\mathbb G\to \mathbb R$ (or more generally a distribution on $\mathbb G$) is $S$-polynomial if for all $X\in S$ there exists $k\in \mathbb N$ such that the iterated derivative $X^k f… Expand
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