Journal of Lie Theory

no. 3
Three-Dimensional Topological Loops with Nilpotent Multiplication Groups
Journal of Lie Theory, Volume 25 (2015) no. 3, pp. 787-805
We describe the structure of indecomposable nilpotent Lie groups which are multiplication groups of three-dimensional simply connected topological loops. In contrast to the 2-dimensional loops there is no connected topological loop of dimension greater than 2 such that the Lie algebra of its multiplication group is an elementary filiform Lie algebra. We determine the indecomposable nilpotent Lie groups of dimension less or equal to 6 and their subgroups which are the multiplication groups and the inner mapping groups of the investigated loops. We prove that all multiplication groups have a 1-dimensional centre and the corresponding loops are centrally nilpotent of class 2.
DOI: 10.5802/jolt.860
Classification: 57S20, 22E25, 20N05, 57M60, 22F30
Keywords: Multiplication group of loops, topological transformation group, nilpotent Lie group 
@article{JOLT_2015_25_3_a7,
     author = {A. Figula and M. Lattuca},
     title = {Three-Dimensional {Topological} {Loops} with {Nilpotent} {Multiplication} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {787--805},
     year = {2015},
     volume = {25},
     number = {3},
     doi = {10.5802/jolt.860},
     zbl = {1331.22007},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.860/}
}
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A. Figula; M. Lattuca. Three-Dimensional Topological Loops with Nilpotent Multiplication Groups. Journal of Lie Theory, Volume 25 (2015) no. 3, pp. 787-805. doi: 10.5802/jolt.860

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