arXiv subjects

Ágota Figula

Publications and source records attributed to Ágota Figula.

23 records · Page 2Linked to original sources

arXiv2015

Extensions of groups by weighted Steiner loops

Solving functional equations given in \cite{nagy} for extensions of a group $A$ by a weighted Steiner loop $S$ we obtain concrete description for all loops with interesting weak associativity properties if the Steiner loop $S$ induces only the trivial automorphism on $A$. We show that the restricted Fischer groups and their geometry play an important role for loop extension with right alternative property. Also the automorphism groups of these extensions as well as the conditions for isomorphisms between two extensions are studied.

math.GR↗

arXiv2015

$3$-dimensional Bol loops corresponding to solvable Lie triple systems

We classify the connected $3$-dimensional differentiable Bol loops $L$ having a solvable Lie group as the group topologically generated by the left translations of $L$ using $3$-dimensional solvable Lie triple systems. Together with \cite{figula} our results complete the classification of all $3$-dimensional differentiable Bol loops.

math.GR↗

arXiv2015

Loops which are semidirect products of groups

We construct loops which are semidirect products of groups of affinities. As their elements in many cases one may take transversal subspaces of an affine space. In particular we obtain in this manner smooth loops having Lie groups of affine real transformations as the groups generated by left translations, whereas the groups generated by right translations are smooth groups of infinite dimension. We also determine the Akivis algebras of these loops.

math.GR↗

arXiv2015

On the multiplication groups of three-dimensional topological loops

We clarify the structure of nilpotent Lie groups which are multiplication groups of $3$-dimensional simply connected topological loops and prove that non-solvable Lie groups acting minimally on $3$-dimensional manifolds cannot be the multiplication group of $3$-dimensional topological loops. Among the nilpotent Lie groups for any filiform groups ${\mathcal F}_{n+2}$ and ${\mathcal F}_{m+2}$ with $n, m > 1$, the direct product ${\mathcal F}_{n+2} \times \mathbb R$ and the direct product ${\mathcal F}_{n+2} \times _Z {\mathcal F}_{m+2}$ with amalgamated center $Z$ occur as the multiplication group of $3$-dimensional topological loops. To obtain this result we classify all $3$-dimensional simply connected topological loops having a $4$-dimensional nilpotent Lie group as the group topologically generated by the left translations.

math.GR↗

arXiv2015

Affine reductive spaces of small dimension and left A-loops

In this paper we determine the at least $4$-dimensional affine reductive homogeneous manifolds for an at most $9$-dimensional simple Lie group or an at most $6$-dimensional semi-simple Lie group. Those reductive spaces among them which admit a sharply transitive differentiable section yield local almost differentiable left A-loops. Using this we classify all global almost differentiable left A-loops $L$ having either a $6$-dimensional semi-simple Lie group or the group $SL_3(\mathbb R)$ as the group topologically generated by their left translations. Moreover, we determine all at most $5$-dimensional left A-loops $L$ with $PSU_3(\mathbb C,1)$ as the group topologically generated by their left translations.

math.DG↗