Derivations and automorphisms of locally matrix algebras and groups
DOI:
https://doi.org/10.15407/dopovidi2020.09.019Keywords:
automorphism, derivation, locally matrix algebraAbstract
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.
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