Ágota Figula

The multiplication groups of 2-dimensional topological loops

Abstract If the multiplication group Mult(L) of a connected simply connected 2-dimensional topological loop L is a Lie group, then Mult(L) is an elementary filiform Lie group ℱ of dimension n + 2 for some n ⩾ 2, and any such group is the multiplication group of a connected simply connected 2-dimensional topological loop L. Moreover, if the group topologically generated by the left translations of L has dimension 3, then L is uniquely determined by a real polynomial of degree n.

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

Abstract Using the relations between affine symmetric spaces and differentiable Bol loops we determine all 3-dimensional connected differentiable proper Bol loops having a non-solvable Lie group as the group topologically generated by their left translations.

The action of a compact Lie group on nilpotent Lie algebras of type {{n,2}}

Abstract We classify finite-dimensional real nilpotent Lie algebras with 2-dimensional central commutator ideals admitting a Lie group of automorphisms isomorphic to SO 2 ⁢ ( ℝ )

Multiplicative loops of 2-dimensional topological quasifields

{{\mathrm{SO}}_{2}(\mathbb{R})}

Some numerical characteristics of Sylvester and Hadamard matrices

. This is the first step to extend the class of nilpotent Lie algebras 𝔥

Three-Dimensional Topological Loops with Solvable Multiplication Groups

{{\mathfrak{h}}}

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

of type { n , 2 }

Affine reductive spaces of small dimension and left A-loops

{\{n,2\}}

ON THE GEOMETRY OF THE DOMAIN OF THE SOLUTION OF NONLINEAR CAUCHY PROBLEM

to solvable Lie algebras in which 𝔥

Loops as sections in compact Lie groups

{{\mathfrak{h}}}