Multiply transitive Lie group of transformations as a~physical structure

V. A. Kyrov

Matematičeskie trudy, Tome 24 (2021) no. 2, pp. 81-104

Résumé

We establish a connection between physical structures and Lie groups and prove that the physical structure of rank ($n+1,2$), $n\in\mathbb{N}$, on a smooth manifold is isotopic to an almost $n$-transitive Lie group of transformations. Afterwards, we prove that an almost $n$-transitive Lie group of transformations is isotopic to a physical structure of rank ($n+1,2$).