Extensions of loops and transformation groups

University of Debrecen

Doctoral School of Mathematical and Computational Sciences

Figula Ágota

mathematics and computing

The main goal is to generalize and to extend the theories, methods and constructions in non-associative structures, which are well-known and famous results in the case of groups. Within Lie theory, special attention is paid to the extension of Lie’s third theorem and Cartan’s theorem for analytic loops. We plan to investigate the global extensibility of local alternative loops. We wish to discuss the generalization of the Schreier extension theory and the cohomology theory for commutative groups to Steiner loops. Our motivation is to obtain effective methods for constructing and classifying Steiner triple systems containing special configurations. A further objective is to generalize the original idea of Sophus Lie, to determine the first order systems of ordinary differential equations allowing a given Lie group as a subgroup of their symmetry group. Our intention is to describe the relations between the geometric properties of nilmanifolds and the algebraic properties of their isometry groups. Within this framework, we also deal with the classification of totally geodesic subgroups.

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University of Debrecen

2026-01-15