Some Theorems on Leibniz Algebras |
| |
Authors: | Donald W Barnes |
| |
Institution: | 1. School of Mathematics and Statistics , University of Sydney , Sydney , Australia donwb@iprimus.com.au |
| |
Abstract: | If U is a subnormal subalgebra of a finite-dimensional Leibniz algebra L and M is a finite-dimensional irreducible L-bimodule, then all U-bimodule composition factors of M are isomorphic. If U is a subnormal subalgebra of a finite-dimensional Leibniz algebra L, then the nilpotent residual of U is an ideal of L. Engel subalgebras of finite-dimensional Leibniz algebras are shown to have similar properties to those of Lie algebras. A subalgebra is shown to be a Cartan subalgebra if and only if it is minimal Engel, provided that the field has sufficiently many elements. |
| |
Keywords: | Engel subalgebras Leibniz algebras Nilpotent Subnormal |
|
|