D. Burde

most citedLeft-symmetric algebras, or pre-Lie algebras in geometry and physics

1 citations · 2 across the 6 of their papers we have counts for

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math.RA2004

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…

math.RA2004

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…

math.RA2004★ 1 cited

On the matrix equation XA-AX=X^p

Dietrich Burde

We study the matrix equation $X A - A X = X^{p}$ in $M_{n} (K)$ for $1 < p < n$ . It is shown that every matrix solution $X$ is nilpotent and that the generalized eigenspaces of $A$ are $X$ -inva…