37 citations · 125 across the 37 of their papers we have counts for
42 papers
Fixed-point-free automorphisms of solvable Lie algebras
Dietrich Burde, Karel Dekimpe
In this paper, we investigate the existence of fixed-point-free automorphisms for finite-dimensional Lie algebras. By a result of Jacobson, a Lie algebra admitting a fixed-point-fr…
The index of nilpotent Lie algebras
Dietrich Burde, Karel Dekimpe
The index of a Lie algebra is an important invariant which arises in several areas, e.g. in the study of coadjoint orbits for a Lie group, in invariant theory and in representation…
Post-Lie algebra structures for perfect Lie algebras
Dietrich Burde, Karel Dekimpe, Mina Monadjem
We study the existence of post-Lie algebra structures on pairs of Lie algebras , where one of the algebras is perfect non-semisimple, and the other one…
Nielsen numbers of affine n-valued maps on nilmanifolds
Charlotte Deconinck, Karel Dekimpe
A nilmanifold is a quotient N\G of a connected and simply connected nilpotent Lie group G by a uniform lattice N. In this paper we determine the Reidemeister and Nielsen number of…
On the rationality of the Nielsen zeta function for maps on solvmanifolds
Karel Dekimpe, Iris Van den Bussche
In [3,9], the Nielsen zeta function has been shown to be rational if is a self-map of an infra-solvmanifold of type (R). It is, however, still unknown whether …
Rigidity results for Lie algebras admitting a post-Lie algebra structure
Dietrich Burde, Karel Dekimpe, Mina Monadjem
We study rigidity questions for pairs of Lie algebras admitting a post-Lie algebra structure. We show that if is semisimple and $\mathf…