Abstract
In the work of M. Hall [1], a certain way of fixing a basis of a free Lie algebra is indicated. However, the concrete bases which one needs to construct, in order to solve certain problems, do not always fall into Hall’s scheme. For instance, the basis of a free Lie algebra considered in the work [2] cannot be constructed using Hall’s method. For this reason, in each such case it is necessary to reprove that a certain subset of a free Lie algebra is a basis. Below, we give a method that generalizes Hall’s method for choosing a basis in a free Lie algebra.
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References
M. Hall, A basis for free Lie rings and higher commutators in free groups, Proc. Amer. Math. Soc. 1 (1950) 575–581.
A.I. Shirshov, On free Lie rings, Mat. Sbornik 45 (1958), no. 2, 113–122.
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© 2009 Birkhäuser Verlag, P.O. Box 133, CH-4010 Basel, Switzerland
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Shirshov, A.I. (2009). On the Bases of a Free Lie Algebra. In: Bokut, L., Shestakov, I., Latyshev, V., Zelmanov, E. (eds) Selected Works of A.I. Shirshov. Contemporary Mathematicians. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8858-4_11
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DOI: https://doi.org/10.1007/978-3-7643-8858-4_11
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