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

Source: [On maximal solvable extensions of a pure non-characteristically nilpotent Lie algebra](<https://www.sota2.com/research/paper/68fa59731e209131ce9b739a>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T15:55:16.464Z

Authors: K.K. Abdurasulov, B.A. Omirov

Published: 2021-11-15T10:20:21.000Z

## 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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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2111.07651>)

[PDF](<https://arxiv.org/pdf/2111.07651.pdf>)