159 citations · 404 across the 61 of their papers we have counts for
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On finite-dimensional homogeneous Lie algebras of derivations of polynomial rings
Ivan Arzhantsev, Sergey Gaifullin, Viktor Lopatkin
For a finite set of homogeneous locally nilpotent derivations of the algebra of polynomials in several variables, a finite dimensionality criterion for the Lie algebra generated by…
Uniqueness of addition in Lie algebras revisited
Ivan Arzhantsev
We obtain new and improve old results on uniqueness of addition in Lie rings and Lie algebras. A Lie ring is called a unique addition ring, or a UA-Lie ring, if any…
Finite-dimensional subalgebras in polynomial Lie algebras of rank one
I. V. Arzhantsev, E. A. Makedonskii, A. P. Petravchuk
Let W_n(K) be the Lie algebra of derivations of the polynomial algebra K[X]:=K[x_1,...,x_n] over an algebraically closed field K of characteristic zero. A subalgebra L of W_n(K) is…
Saturated subfields and invariants of finite groups
Ivan V. Arzhantsev, Anatoliy P. Petravchuk
Every subfield $\kk(ϕ)$ of the field of rational functions $\kk(x_1,...,x_n)$ is contained in a unique maximal subfield of the form $\kk(ψ)$. The element is called generative f…