Nurtas Shyntas

Standard identities for polynomial vector fields

Let $W_n$ be the Lie algebra of polynomial vector fields in $n$ variables over a field of characteristic zero, and let $s_k$ denote the alternating sum of compositions of $k$ vector fields. The identity $s_{n^2+2n-1}=0$ has been asserted for arbitrary $n$. We give an explicit counterexample in dimension five, verified...