Geodesic
Three-Dimensional Topological Loops with Nilpotent Multiplication Groups
Journal of Lie theory, Tome 25 (2015) no. 3, pp. 787-805
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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.
Classification : 57S20, 22E25, 20N05, 57M60, 22F30
Mots-clés : Multiplication group of loops, topological transformation group, nilpotent Lie group 
@article{JLT_2015_25_3_JLT_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},
     url = {http://geodesic.mathdoc.fr/item/JLT_2015_25_3_JLT_2015_25_3_a7/}
}
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A. Figula; M. Lattuca. Three-Dimensional Topological Loops with Nilpotent Multiplication Groups. Journal of Lie theory, Tome 25 (2015) no. 3, pp. 787-805. http://geodesic.mathdoc.fr/item/JLT_2015_25_3_JLT_2015_25_3_a7/