Zero divisors in enveloping algebras of graded Lie algebras (Q1072160)

Let k be a field of characteristic different from 2. Following \textit{R. Bøgvad} [Astérisque 113/114, 156-166 (1984; Zbl 0552.17012)], a graded Lie algebra over k, \(L=\oplus_{i\geq 1}L_ i\), is torsion free if [x,x]\(\neq 0\) for every nonzero x of odd degree and absolutely torsion free if it remains torsion free after field extension to the algebraic closure \(\bar k\) of k. The authors prove: the enveloping algebra UL of an absolutely torsion free graded Lie algebra L has no zero divisors. In an appendix they reproduce a different proof due to R. Bøgvad.