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 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 |F|ℵ0, where |F| is the cardinality of the field F.