On maximal solvable extensions of a pure non-characteristically nilpotent Lie algebra
Rings and Algebras
2022-07-21 v5
Abstract
In this paper we introduce the notion of pure non-characteristically nilpotent Lie algebra and under a condition we prove that a complex maximal extension of a finite-dimensional pure non-characteristically nilpotent Lie algebra is isomorphic to a semidirect sum of the nilradical and its maximal torus. We also prove that such solvable Lie algebras are complete and we specify a subclass of the maximal solvable extensions of pure non-characteristically nilpotent Lie algebras that have trivial cohomology group. Some comparisons with the results obtained earlier are given.
Keywords
Cite
@article{arxiv.2111.07651,
title = {On maximal solvable extensions of a pure non-characteristically nilpotent Lie algebra},
author = {K. K. Abdurasulov and B. A. Omirov},
journal= {arXiv preprint arXiv:2111.07651},
year = {2022}
}