Lie solvable enveloping algebras of characteristic two

Lie solvable restricted enveloping algebras were characterized by Riley and Shalev except when the ground field is of characteristic 2. We resolve the characteristic 2 case here which completes the classification. As an application of our result, we obtain a characterization of ordinary Lie algebras over any field whose enveloping algebra is Lie solvable

Solvable Leibniz algebras with triangular nilradical

A classification exists for Lie algebras whose nilradical is the triangular Lie algebra $T(n)$. We extend this result to a classification of all solvable Leibniz algebras with nilradical $T(n)$. As an example we show the complete classification of all Leibniz algebras whose nilradical is $T(4)$.Comment: arXiv admin note: text overlap with arXiv:1307.844

Half-flat structures on indecomposable Lie groups

This article can be viewed as a continuation of the articles arXiv:0912.3486 and arXiv:1012.3714 where the decomposable Lie algebras admitting half-flat SU(3)-structures are classified. The new main result is the classification of the indecomposable six-dimensional Lie algebras with five-dimensional nilradical which admit a half-flat SU(3)-structure. As an important step of the proof, a considerable refinement of the classification of six-dimensional Lie algebras with five-dimensional non-Abelian nilradical is established. Additionally, it is proved that all non-solvable six-dimensional Lie algebras admit half-flat SU(3)-structures.Comment: 25 pages, v2: minor corrections due to the new classification of the six-dimensional Lie algebras with five-dimensional nilradical by Shabanskay