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arXiv · 2111.07651

On maximal solvable extensions of a pure non-characteristically nilpotent Lie algebra

K. K. Abdurasulov·B. A. Omirov
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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.

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K. K. Abdurasulov, B. A. Omirov. 2021-11-15. On maximal solvable extensions of a pure non-characteristically nilpotent Lie algebra. https://arxiv.org/abs/2111.07651

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