Derivations and automorphisms of locally matrix algebras

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 $\mathbb{F}.$