On generators of $L/R^ 2$ Lie algebras
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- by Vladimir Shpilrain
- Proc. Amer. Math. Soc. 119 (1993), 1039-1043
- DOI: https://doi.org/10.1090/S0002-9939-1993-1154249-X
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Abstract:
Let $L$ be a free Lie algebra of finite rank $n$ and $R$ its arbitrary ideal. A necessary and sufficient condition for $n$ elements of the Lie algebra $L/{R^2}$ to be a generating set is given. In particular, we have a criterion for $n$ elements of a free Lie algebra of rank $n$ to be a generating set which is similar to the corresponding group-theoretic result due to Birman (An inverse function theorem for free groups, Proc. Amer. Math. Soc. 41 (1973), 634-638).References
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Bibliographic Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 119 (1993), 1039-1043
- MSC: Primary 17B01; Secondary 17B40
- DOI: https://doi.org/10.1090/S0002-9939-1993-1154249-X
- MathSciNet review: 1154249