Fields of interest:
The main focus of my research lies in the area of Lie groups, Lie algebras and Representation theory. My current research project "Geometric Structures on Lie Groups" studies geometric structures on manifolds which are locally modelled on homogeneous spaces. Many familiar geometric structures are of this type. An important question is to find a criterion for the existence of such structures on a given manifold or Lie group. Related topics are crystallographic actions, simply transitive affine actions of Lie groups and important generalizations of these. The methods here are mainly of algebraic nature, using cohomology and representation theory, deformation and degeneration theory, and the study of certain Lie-admissible algebra structures.
- Periodic derivations and prederivations of Lie algebras, (with W. Moens), Journal of Algebra, Vol. 357, 208-221 (2012).
- Post-Lie algebra structures and generalized derivations of semisimple Lie algebras, (with K. Dekimpe), Moscow Mathematical Journal, Vol. 13, Issue 1, 1-18 (2013).
- Classification of orbit closures in the variety of 3-dimensional Novikov algebras, (with T. Benes), Journal of Algebra and Its Applications, Vol. 13, Issue 02, 1350081 (2014).