Abstract
The composition method was developed by A. I. Shirshov. To begin with, in [372], he proved the theorem on embedding a Lie algebra of finite or countable dimension into a two-generated Lie algebra, applying this method. In [278], the notion of a composition was introduced and a lemma, the first variant of a composition lemma, was proven (see [278], Lemma 4). The composition lemma in its modern form appeared in the work of L. A. Bokut’ [53]. Therein A. I. Shirshov also presented applications of the method in deciding the word problem for Lie algebras given by generators and defining relations and to studying one-relator Lie algebras. Next, in [373] he employed the composition method in his constructing a basis of the amalgamated free product of Lie algebras.
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References
A. I. Shirshov [372], [373], [377], [378]
L. A. Bokut’ [53], [54], [70], [72], [73], [74], [75], [78], [81]
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S. Maclane [252]
D. B. Fuchs [143]
N. Jacobson [177]
O. Zariski and P. Samuel [430]
E. S. Golod [153]
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© 1994 Springer Science+Business Media Dordrecht
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Bokut’, L.A., Kukin, G.P. (1994). The Composition Method in the Theory of Lie Algebras. In: Algorithmic and Combinatorial Algebra. Mathematics and Its Applications, vol 255. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2002-9_3
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DOI: https://doi.org/10.1007/978-94-011-2002-9_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4884-2
Online ISBN: 978-94-011-2002-9
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