Derivations and automorphisms of locally matrix algebras and groups

TitleDerivations and automorphisms of locally matrix algebras and groups
Publication TypeJournal Article
Year of Publication2020
AuthorsBezushchak, OO
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
Date Published9/2020

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 |0 , 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.

Keywordsautomorphism, derivation, locally matrix algebra

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