## Zero divisors in enveloping algebras of graded Lie algebras.(English)Zbl 0587.55006

Let k be a field of characteristic different from 2. Following 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.
Reviewer: J.C.Thomas

### MSC:

 55Q52 Homotopy groups of special spaces 57T05 Hopf algebras (aspects of homology and homotopy of topological groups) 17B70 Graded Lie (super)algebras 17B35 Universal enveloping (super)algebras

Zbl 0552.17012
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### References:

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