arXiv subjects
Publications and source records attributed to L. Garcia Vergnolle.
The quasi-filiform Lie algebras of nonzero rank are described. The classifications of filiform and quasi-filiform naturally graded algebras are corrected.
We determine the isomorphism classes of Jordan algebras in dimension two over the field of real numbers. Using techniques of non-standard analysis we study the properties of the variety of Jordan algebras, and also the contractions among these algebras.
We present all real solvable algebraically rigid Lie algebras of dimension $n\leq 8$. The difference between the classification of complex and real rigid Lie algebras is analyzed.
We show that a solvable real rigid Lie algebra is not completelt rigid, by constructing an example of minimal dimension where the external torus is not spanned by $ad$-semisimple derivations over $\mathbb{R}$. We analyze the real forms of nilradicals of solvable rigid Lie algebras in dimensions $n\leq 7$ and give the real classification for dimension 8.