The maximal abelian dimension of a Lie algebra, Rentschler's property and Milovanov's conjecture (Q2188401)

Let \(L\) be a Lie algebra of dimension \(n\) and \(S(L)\) be its symmetric algebra. This paper is devoted to finding solvable Lie algebras which satisfy Milovanov's conjecture; which is, for any solvable Lie algebra, \(L\), there exists a complete Poisson commutative subalgebra of \(S(L)\) generated by elements of degree two. The paper is devoted to showing that certain classes of filiform Lie algebras satisfy this conjecture,