On the Lie structure of locally matrix algebras

Keywords: locally matrix algebra, derivation
Published online: 2020-10-20

Abstract


Let $A$ be a unital locally matrix algebra over a field $\mathbb{F}$ of characteristic different from $2.$ We find a 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.

Article metrics
PDF downloads: 326
Abstract views: 474
How to Cite
(1)
Bezushchak O. On the Lie Structure of Locally Matrix Algebras. Carpathian Math. Publ. 2020, 12 (2), 311-316.