L. A. Simonian | Searcharxiv

arXiv2003

Structure Theory for One Class of Locally Finite Lie Algebras

In this paper I consider locally finite Lie algebras of characteristic zero satisfying the condition that for every finite number of elements $x_{1}, x_{2},..., x_{k}$ of such an algebra $L$ there is finite-dimensional subalgebra $A$ which contains these elements and $L(adA)^n\subset A$ for some integer $n$. For such algebras I prove several structure theorems that can be regarded as generalizations of the classical structure theorems of the finite-dimensional Lie algebras theory.

math.RA↗

arXiv1999

The Embedding Theorem for a Mixed Verbal Wreath Product in Lie Algebras Representations

The mixed verbal wreath product in representations of Lie algebras is a construction parallel to the verbal wreath product of Lie algebras introduced by A. L. Shmelkin. It is shown that the analog of the group theorem on embedding in the verbal wreath product also holds for representations of Lie algebras.

math.RA↗