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

  • A. P. Petravchuk Kyiv Nat. Taras Shevchenko Univ., Ukraine


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.
How to Cite
Petravchuk, A. P. “On the Sum of an Almost Abelian Lie Algebra and a Lie Algebra Finite-Dimensional over Its Center”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 51, no. 5, May 1999, pp. 636–644, https://umj.imath.kiev.ua/index.php/umj/article/view/4650.
Research articles