9 citations · 29 across the 19 of their papers we have counts for
22 papers
On minimal ideals of Lie algebras
Donald W. Barnes
We show that a minimal ideal of a finite-dimensional Lie algebra is either simple or abelian.
Faithful irreducible representations of modular Lie algebras
Donald W. Barnes
Let L be a finite-dimensional Lie algebra over a field of non-zero characteristic. By a theorem of Jacobson, L has a finite-dimensional faithful module which is completely reducibl…
On -hypercentral modules and character clusters
Donald W. Barnes
Let be a saturated formation of soluble Lie algebras over a field of characteristic and let denote the field of elements. Let $(L,[p])…
Faithful completely reducible representations of modular Lie algebras
Donald W. Barnes
The Ado-Iwasawa Theorem asserts that a finite-dimensional Lie algebra over a field has a finite-dimensional faithful module . There are several extensions asserting the…
Conditions for a Schunck class to be a formation
Donald W. Barnes
A Schunck class H is determined by the class X of primitives contained in H. We give necessary and sufficient conditions on X for H to be a saturated formation.
Blocks of representations of Lie algebras
Donald W. Barnes
In the theory of finite groups, the irreducible representations of G over a field F are classified into blocks based on a direct decompositions of the group algebra FG. This gives…