Derivations and automorphisms of locally matrix algebras and groups - Bezushchak, O.O. (Reports of the National Academy of Sciences of Ukraine, 2020)
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. Let A* be the group of invertible elements of a unital locally matrix algebra A. We describe isomorphisms of groups [A*, A*]. In particular, we show that inductive limits of groups SLn(F) are determined by their Steinitz numbers.