1 citations · 2 across the 6 of their papers we have counts for
6 papers
Left-symmetric algebras, or pre-Lie algebras in geometry and physics
Dietrich Burde
In this survey article we discuss the origin, theory and applications of left-symmetric algebras (LSAs in short) in geometry in physics. Recently Connes, Kreimer and Kontsevich hav…
The Auslander conjecture for NIL-affine crystallographic groups
Dietrich Burde, Karel Dekimpe, Sandra Deschamps
Let N be a simply connected, connected real nilpotent Lie group of finite dimension n. We study subgroups in $\Aff (N)=N\rtimes \Aut (N)$ acting properly discontinuously and co…
Lie Algebra Prederivations and strongly nilpotent Lie Algebras
Dietrich Burde
We study Lie algebra prederivations. A Lie algebra admitting a non-singular prederivation is nilpotent. We classify filiform Lie algebras admitting a non-singular prederivation but…
Degenerations of 7-dimensional nilpotent Lie algebras
Dietrich Burde
We study the varieties of Lie algebra laws and their subvarieties of nilpotent Lie algebra laws. We classify all degenerations of (almost all) five-step and six-step nilpotent seve…
Characteristically nilpotent Lie algebras and symplectic structures
Dietrich Burde
We study symplectic structures on characteristically nilpotent Lie algebras (CNLAs) by computing the cohomology space $H^2(\Lg,k)$ for certain Lie algebras $\Lg$. Among these Lie a…
On the matrix equation XA-AX=X^p
Dietrich Burde
We study the matrix equation in for . It is shown that every matrix solution is nilpotent and that the generalized eigenspaces of are -inva…