Derivations and automorphisms of locally matrix algebras

2020/07/30 by Bezushchak, Oksana · 1 citation
#15A69 #16W20 #16W25 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2007.15716

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 \mathbbF 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 |\mathbbF|^ℵ₀, where |\mathbbF| is the cardinality of the field \mathbbF.

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