On Strongly Inert Subalgebras of an Infinite-Dimensional Lie Algebra

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

Abstract

We study infinite-dimensional Lie algebras L over an arbitrary field that contain a subalgebra A such that dim(A + [A, L])/A < ∞. We prove that if an algebra L is locally finite, then the subalgebra A is contained in a certain ideal I of the Lie algebra L such that dimI/A <. We show that the condition of local finiteness of L is essential in this statement.
Published
25.07.2002
How to Cite
PetravchukA. P. “On Strongly Inert Subalgebras of an Infinite-Dimensional Lie Algebra”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 54, no. 7, July 2002, pp. 1025-8, https://umj.imath.kiev.ua/index.php/umj/article/view/4143.
Section
Short communications