Three-Dimensional Topological Loops with Nilpotent Multiplication Groups

Margherita Lattuca, Ágota Figula

Risultato della ricerca: Articlepeer review

3 Citazioni (Scopus)

Abstract

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.
Lingua originaleEnglish
pagine (da-a)787-805
Numero di pagine19
RivistaJournal of Lie Theory
Volume25
Stato di pubblicazionePublished - 2015

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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