Three-dimensional loops as sections in a four-dimensional solvable Lie group

zbMATH Open1295.22008arXiv1507.00631MaRDI QIDQ5418417

Ágota Figula

Publication date: 3 June 2014

Abstract: We classify all three-dimensional connected topological loops such that the group topologically generated by their left translations is the four-dimensional connected Lie group $G$ which has trivial center and precisely two one-dimensional normal subgroups. We show that $G$ is not the multiplication group of connected topological proper loops.

Full work available at URL: https://arxiv.org/abs/1507.00631

zbMATH Keywords

multiplication group of a loopsharply transitive sections in groups

Mathematics Subject Classification ID

Lie groups (22E99) Other topological algebraic systems and their representations (22A30)

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3-dimensional Bol loops as sections in non-solvable Lie groups

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