In this paper 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 ≥ 3 such that the Lie algebra of its multiplication group is an elementary filiform Lie algebra. We determine the indecomposable nilpotent Lie groups of dimension ≤ 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 1-dimensional centre and the corresponding loops are centrally nilpotent of class 2.
|Numero di pagine||19|
|Rivista||Journal of Lie Theory|
|Stato di pubblicazione||Published - 2015|
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory