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On the sum of an almost abelian Lie algebra and a Lie algebra finite-dimensional over its center

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Ukrainian Mathematical Journal Aims and scope

Abstract

We consider a Lie algebraL over an arbitrary field that is decomposable into the sumL=A+B of an almost Abelian subalgebraA and a subalgebraB finite-dimensional over its center. We prove that this algebra is almost solvable, i.e., it contains a solvable ideal of finite codimension. In particular, the sum of the Abelian and almost Abelian Lie algebras is an almost solvable Lie algebra.

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Authors
  1. A. P. Petravchuk
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Additional information

Kiev University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 5, pp. 636–644, May, 1999.

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Petravchuk, A.P. On the sum of an almost abelian Lie algebra and a Lie algebra finite-dimensional over its center. Ukr Math J 51, 707–715 (1999). https://doi.org/10.1007/BF02591706

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  • DOI: https://doi.org/10.1007/BF02591706

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