arXiv subjects

Donald W. Barnes

Publications and source records attributed to Donald W. Barnes.

24 records · Page 2Linked to original sources

arXiv2008

Engel subalgebras of Leibniz algebras

Engel subalgebras of finite-dimensional Leibniz algebras are shown to have similar properties to those of Lie algebras. Using these, it is shown that a left Leibniz algebra, all of whose maximal subalgebras are right ideals, is nilpotent. A primitive Leibniz algebra is shown to split over its minimal ideal and that all the complements to its minimal ideal are conjugate. 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. Cartan subalgebras are shown to have a property analogous to intravariance.

math.RA↗

arXiv2007

Lie algebra F-normalisers are intravariant

Let F be a saturated formation of soluble Lie algebras and let U be an F-normaliser of the soluble Lie algebra L. Then U is intravariant in L.

math.RA↗

arXiv2007

On (n+2)-dimensional n-Lie algebras

I show that an (n+2)-dimensional n-Lie algebra over an algebraically closed field must have a subalgeba of codimension 1.

math.RA↗

arXiv2006

Schunck classes of soluble restricted Lie algebras

Schunck classes, saturated formations and projectors were originally defined for finite soluble groups for which they provided families of intravariant subgroups. In this paper, I set out the analogous theory for finite-dimensional soluble restricted Lie algebras and investigate its links to the corresponding theory for ordinary Lie algebras over the same field.

math.RA↗

arXiv2006

Engel subalgebras of n-Lie algebras

Engel subalgebras of finite-dimensional n-Lie algebras are shown to have similar properties to those of Lie algebras. Using these, it is shown that an n-Lie algebra, all of whose maximal subalgebras are ideals, is nilpotent. A primitive 2-soluble n-Lie algebra is shown to split over its minimal ideal and that all the complements to its minimal ideal are conjugate. 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. Cartan subalgebras are shown to have a property analogous to intravariance.

math.RA↗

arXiv2006

On Sikora's spectral sequences

The Swan, Leray and Leray-Serre spectral sequences of a compact Hausdorff HLC space acted on by a discrete group are shown to be isomorphic.

math.AT↗