Aubry, Marc; Lemaire, Jean-Michel Zero divisors in enveloping algebras of graded Lie algebras. (English) Zbl 0587.55006 J. Pure Appl. Algebra 38, 159-166 (1985). 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 Cited in 22 Documents 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 Keywords:graded Lie algebra; absolutely torsion free; enveloping algebra; zero divisors Citations:Zbl 0552.17012 PDF BibTeX XML Cite \textit{M. Aubry} and \textit{J.-M. Lemaire}, J. Pure Appl. Algebra 38, 159--166 (1985; Zbl 0587.55006) Full Text: DOI OpenURL References: [1] Anick, D., Non-commutative algebras and their Hilbert series, J. algebra, 78, 120-140, (1982) · Zbl 0502.16002 [2] Borho, W.; Rentschler, R., Oresche teilmengen in einhüllenden algebren, Math. ann., 217, 201-210, (1975) · Zbl 0297.17004 [3] R. Bøgvad, Some elementary results on the cohomology of graded Lie algebras, in: Homotopie Algébrique et Algèbre Locale, Astérisque 113-114, 156-166. [4] Halperin, S., Finiteness in the minimal models of Sullivan, Trans. A.M.S., 230, 173-199, (1977) · Zbl 0364.55014 [5] Halperin, S.; Lemaire, J.M., Suites inertes dans LES algèbres de Lie graduées, (), no. 22 · Zbl 0655.55004 [6] Milnor, J.; Moore, J.C., On the structure of Hopf algebras, Ann. math., 81, 211-264, (1965) · Zbl 0163.28202 [7] Stenström, B., Rings of quotients, () · Zbl 0194.06602 [8] Sjödin, G., A set of generators for ext_{R} (k, k), Math. scand., 38, 199-210, (1976) · Zbl 0346.18017 [9] Wall, C.T.C., Nets of conics, Math. proc. Cambridge ph. soc., 81, 351-364, (1977) · Zbl 0351.14032 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.