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arXiv · 2012.10178

On derivations and low-dimensional (co)homology groups of pro-sovable Lie algebras associated with $\mathbf{n}_1$ and $\mathbf{n}_2$

K. K. Abdurasulov·I. S. Rakhimov·G. O. Solijanova
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Abstract

In the paper we describe the derivations of two $\mathbb{N}$-graded infinity-dimensional Lie algebras $\mathbf{n}_1$ and $\mathbf{n}_1$ what are positive parts of affine Kats-Moody algebras $A^{(1)}_1$ and $A^{(2)}_2$, respectively. Then we construct all pro-solvable Lie algebras whose potential nilpotent ideals are $\mathbf{n}_1$ and $\mathbf{n}_2$. For two specific representatives of these classes low-dimensional (co)homology groups are computed.

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K. K. Abdurasulov, I. S. Rakhimov, G. O. Solijanova. 2020-12-18. On derivations and low-dimensional (co)homology groups of pro-sovable Lie algebras associated with $\mathbf{n}_1$ and $\mathbf{n}_2$. https://arxiv.org/abs/2012.10178

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