Journal of Lie Theory

no. 4
Actions of R.widetilde(SL2R) on Laguerre Planes Related to the Moulton Planes
Journal of Lie Theory, Volume 17 (2007) no. 4, pp. 685-708
We construct flat Laguerre planes that admit the universal covering group of SL2R, extended by a factor R, as a group of automorphisms. These planes contain the affine Moulton planes as derived planes, and they are constructed by gluing together two copies of a Moulton plane, folded up along their fixed lines. The action of the Moulton group carries over (modulo Z2) to the Laguerre planes, and the circles and parallel classes are essentially orbits of 4 types of one-parameter groups of the Moulton action. These planes have group dimension 4 and also provide examples of flat Laguerre planes of Kleinewillinghöfer type II.G.1.
DOI: 10.5802/jolt.470
Classification: 51H15, 51B15, 22E46
Keywords: Universal cover of the unimodular group, Moulton plane, Moulton group, Laguerre plane 
@article{JOLT_2007_17_4_a0,
     author = {R. L\"owen and G. F. Steinke},
     title = {Actions of {R.widetilde(SL\protect\textsubscript{2}R)} on {Laguerre} {Planes} {Related} to the {Moulton} {Planes}},
     journal = {Journal of Lie Theory},
     pages = {685--708},
     year = {2007},
     volume = {17},
     number = {4},
     doi = {10.5802/jolt.470},
     zbl = {1155.51008},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.470/}
}
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%A G. F. Steinke
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R. Löwen; G. F. Steinke. Actions of R.widetilde(SL2R) on Laguerre Planes Related to the Moulton Planes. Journal of Lie Theory, Volume 17 (2007) no. 4, pp. 685-708. doi: 10.5802/jolt.470

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