59 citations · 318 across the 39 of their papers we have counts for
7 papers · 1 filter
A Lie algebra that can be written as a sum of two nilpotent subalgebras, is solvable
Pasha Zusmanovich
This is an old paper put here for archeological purposes. It is proved that a finite-dimensional Lie algebra over a field of characteristic p>5, that can be written as a vector spa…
On the utility of Robinson-Amitsur ultrafilters
Pasha Zusmanovich
An embedding theorem for algebraic systems is presented, basing on a certain old ultrafilter construction. As an application, we outline alternative proofs of some results from the…
Commutative 2-cocycles on Lie algebras
Askar Dzhumadil'daev, Pasha Zusmanovich
On Lie algebras, we study commutative 2-cocycles, i.e., symmetric bilinear forms satisfying the usual cocycle equation. We note their relationship with antiderivations and compute…
On -derivations of Lie algebras and superalgebras
Pasha Zusmanovich
We study -derivations -- a construction simultaneously generalizing derivations and centroid. First, we compute -derivations of current Lie algebras and of modular Zassenhaus…
The alternative operad is not Koszul
Askar Dzhumadil'daev, Pasha Zusmanovich
Using computer calculations, we prove the statement in the title.
Nonexistence of invariant symmetric forms on generalized Jacobson-Witt algebras revisited
Pasha Zusmanovich
We provide a short alternative homological argument showing that any invariant symmetric bilinear form on simple modular generalized Jacobson-Witt algebras vanishes, and outline an…