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arXiv · 2007.15716

Derivations and automorphisms of locally matrix algebras

Oksana Bezushchak
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Abstract

We describe derivations and automorphisms of infinite tensor products of matrix algebras. Using this description we show that for a countable--dimensional locally matrix algebra $A$ over a field $\mathbb{F}$ the dimension of the Lie algebra of outer derivations of $A$ and the order of the group of outer automorphisms of $A$ are both equal to $|\mathbb{F}|^{\aleph_0},$ where $|\mathbb{F}|$ is the cardinality of the field $\mathbb{F}.$

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Oksana Bezushchak. 2020-07-30. Derivations and automorphisms of locally matrix algebras. https://arxiv.org/abs/2007.15716

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