
Journal of Lie Theory 25 (2015), No. 3, 787805 Copyright Heldermann Verlag 2015 ThreeDimensional Topological Loops with Nilpotent Multiplication Groups Ágota Figula Institute of Mathematics, University of Debrecen, P.O.B. 12, 4010 Debrecen, Hungary figula@math.klte.hu Margherita Lattuca Dip. di Fisica e Chimica, Università degli Studi di Palermo, 91023 Palermo, Via Archirafi 36, Italy margherita.lattuca@unipa.it We describe the structure of indecomposable nilpotent Lie groups which are multiplication groups of threedimensional simply connected topological loops. In contrast to the 2dimensional 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 1dimensional centre and the corresponding loops are centrally nilpotent of class 2. Keywords: Multiplication group of loops, topological transformation group, nilpotent Lie group. MSC: 57S20, 22E25, 20N05, 57M60, 22F30 [ Fulltextpdf (312 KB)] for subscribers only. 