Drittmittelprojekte


  1. Doktoratskolleg: Initiativkolleg 1008-N: Differential Geometry and Lie Groups.
    Speaker: Peter Michor.
    Duration: 01.10.2006-30.09.2009.
    Two positions: Wolfgang Moens, Thomas Benes.

  2. FWF Einzelprojekt P21683: Geometric Structures on Lie Groups.
    Duration: 01.10.2009-30.09.2013.
    Postdoc position (Wolfgang Moens);
    Predoc position (Felix Behringer).

    In this research project we study geometric structures on manifolds which are locally modelled on homogeneous spaces. Many familiar geometric structures are of this type. An important (unsolved) 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.
    Some of these algebraic structures have also applications in quantum mechanics.


    3. Project Publications:



    Degenerations of pre-Lie algebras, D. Burde, T. Benes,
    Journal of Mathematical Physics 50, 112102 (2009).
    arXiv:0809.2188v1 (2008).

    Complete LR-structures on solvable Lie algebras, D. Burde, K. Dekimpe, K. Vercammen,
    Journal of Group Theory 13, Issue 5, 703-719 (2010).
    arXiv:0906.1151v1 (2009).

    Abelian ideals of maximal dimension for solvable Lie algebras, D. Burde, C. Ceballos,
    Journal of Lie Theory 22, No. 3, 741-756 (2012).
    arXiv:0911.2995v2 (2011).

    A Characterization of nilpotent Lie algebras by invertible Leibniz-derivations, W. A. Moens,
    To appear in Communications in Algebra 41, Issue 7 (2013).
    arXiv:1011.6186v1 (2010).

    Faithful Lie algebra modules and quotients of the universal enveloping algebra, D. Burde, W. A. Moens,
    Journal of Algebra, Vol. 325, Issue 1, 440-460 (2011).
    arXiv:1006.2062v1 (2010).

    Affine actions on Lie groups and post-Lie algebra structures, D. Burde, K. Dekimpe, K. Vercammen,
    Linear Algebra and its Applications 437, 1250-1263 (2012).
    arXiv:1109.0251v1 (2011).

    Classification of Novikov algebras, D. Burde, W. A. de Graaf,
    Applicable Algebra in Engineering, Communication and Computing, Vol. 24, Issue 1,1-15 (2013).
    arXiv:1106.5954v1 (2011).

    Post-Lie algebra structures and generalized derivations of semisimple Lie algebras, D. Burde, K. Dekimpe,
    To appear in Moscow Mathematical Journal Vol. 13, Issue 1, 1-18 (2013).
    arXiv:1108.5950v1 (2011).

    Periodic derivations and prederivations of Lie algebras, D. Burde, W. A. Moens,
    Journal of Algebra, Vol. 357, Issue 1, 208-221 (2012).
    arXiv:1108.3548v1 (2011).

    Classification of orbit closures in the variety of 3-dimensional Novikov algebras, D. Burde, T. Benes,
    arXiv:1205.5714v1 (2012).

    Derived length and nildecomposable Lie algebras, D. Burde,
    arXiv:1212.3113 (2012).