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arXiv · 2008.04955

On the Lie structure of locally matrix algebras

Oksana Bezushchak
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Abstract

Let $A$ be a unital locally matrix algebra over a field $\mathbb{F}$ of characteristic different from $2.$ We find necessary and sufficient condition for the Lie algebra $A\diagup\mathbb{F}\cdot 1$ to be simple and for the Lie algebra of derivations $\text{Der}(A)$ to be topologically simple. The condition depends on the Steinitz number of $A$ only.

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Oksana Bezushchak. 2020-08-11. On the Lie structure of locally matrix algebras. https://arxiv.org/abs/2008.04955

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