Dietrich Burde
Homepage: http://homepage.univie.ac.at/Dietrich.Burde/
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.
Selected publications
- Left-symmetric algebras, or pre-Lie algebras in geometry and physics, Cent. Eur. J. Math. 4, no. 3, 323--357 (2006).
- Contractions of Lie algebras and algebraic groups, Archivum Mathematicum 43, no. 5, 321-332 (2007).
- Novikov algebras and Novikov structures on Lie algebras, Linear Algebra and its Appl. 429, no. 1, 31-41 (2008).
- Affine actions on nilpotent Lie groups, (with K. Dekimpe, S. Deschamps), Forum Math. 21, no. 5, 921-934 (2009).
- Computing faithful representations for nilpotent Lie algebras, (with B. Eick, W. A. de Graaf), Journal of Algebra 322, no. 3, 602-612 (2009).
- Degenerations of pre-Lie algebras, (with T. Benes), Journal of Mathematical Physics 50, no. 1, 9 pages (2009).