2 citations · 3 across the 6 of their papers we have counts for
6 papers
Bracket width of current Lie algebras
Boris Kunyavskii, Ievgen Makedonskyi, Andriy Regeta
The length of an element of a Lie algebra is defined as the smallest number needed to represent as a sum of brackets. The bracket width of is defined as sup…
Bracket width of the Lie algebra of vector fields on a smooth affine curve
Ievgen Makedonskyi, Andriy Regeta
We prove that the bracket width of the simple Lie algebra of vector fields of a smooth irreducible affine curve with a trivial tangent sheaf is at most three. In…
On finite-dimensional subalgebras of derivation Lie algebras
Ievgen Makedonskyi
Let be a field, be an associative and commutative -algebra and be a Lie algebra over . We give some descriptions of injections from …
On nilpotent and solvable Lie algebras of derivations
Ie. O. Makedonskyi, A. P. Petravchuk
Let K be a field and A be a commutative associative K-algebra which is an integral domain. The Lie algebra Der A of all K-derivations of A is an A-module in a natural way and if R…
On finite dimensional Lie algebras of planar vector fields with rational coefficients
Ievgen Makedonskyi, Anatoliy Petravchuk
The Lie algebra of planar vector fields with coefficients from the field of rational functions over an algebraically closed field of characteristic zero is considered. We find all…
On noncommutative bases of the free module
Ievgen Makedonskyi
Let be an algebraically closed field of characteristic zero and the polynomial ring in variables over We study bases of…