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arXiv · 2202.10718

Extensions of solvable Lie algebras with naturally graded filiform nilradical

A. Kh. Khudoyberdiyev·S. A. Sheraliyeva
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Abstract

In this work we consider extensions of solvable Lie algebras with naturally graded filiform nilradicals. Note that there exist two naturally graded filiform Lie algebras $n_{n, 1}$ and $Q_{2n}.$ We find all one-dimensional central extensions of the algebra $n_{n, 1}$ and show that any extension of $Q_{2n}$ is split. After that we find one-dimensional extensions of solvable Lie algebras with nilradical $n_{n, 1}$. We prove that there exists a unique non-split central extension of solvable Lie algebras with nilradical $n_{n, 1}$ of maximal codimension. Moreover, all one-dimensional extensions of solvable Lie algebras with nilradical $n_{n, 1}$ whose codimension is equal to one are found and compared these solvable algebras with the solvable algebras with nilradicals are one-dimensional central extension of algebra $n_{n, 1}$.

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A. Kh. Khudoyberdiyev, S. A. Sheraliyeva. 2022-02-22. Extensions of solvable Lie algebras with naturally graded filiform nilradical. https://arxiv.org/abs/2202.10718

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