Journal of Lie Theory

no. 1
Jet Spaces as Nonrigid Carnot Groups
Journal of Lie Theory, Volume 15 (2005) no. 1, pp. 341-356
We define a product on the jet spaces Jk(Rm , Rn) which makes them Carnot groups. The Carnot group contact structure coincides with the classical contact structure in the Lie-Bäcklund setting. Therefore, by prolongation, they are nonrigid Carnot groups, meaning that the space of contact maps is infinite dimensional. We also show that strata dimensions are not rigidity invariants. This is demonstrated by constructing two distinct Carnot groups with strata dimensions (3, 2, 1) but with opposite rigidity.
DOI: 10.5802/jolt.379
Classification: 53C24, 22E25
Keywords: Carnot group, jet space, rigidity 
@article{JOLT_2005_15_1_a23,
     author = {B. Warhurst},
     title = {Jet {Spaces} as {Nonrigid} {Carnot} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {341--356},
     year = {2005},
     volume = {15},
     number = {1},
     doi = {10.5802/jolt.379},
     zbl = {1079.53062},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.379/}
}
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B. Warhurst. Jet Spaces as Nonrigid Carnot Groups. Journal of Lie Theory, Volume 15 (2005) no. 1, pp. 341-356. doi: 10.5802/jolt.379

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