论文标题
局部基质代数的派生和自动形态
Derivations and automorphisms of locally matrix algebras
论文作者
论文摘要
我们描述了基质代数的无限张量产物的推导和自动形态。使用此描述，我们表明，对于一个可计数的 - 局部矩阵代数$ a $在字段上$ \ mathbb {f} $ $ a $ a $的外部衍生物的维度和$ a $ $ a $的外部自动形态的顺序均等于$ | \ m m i \ \ m i \ | $ | \ mathbb {f} | $是字段的基数$ \ mathbb {f}。$
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 $\mathbb{F}$ 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 $|\mathbb{F}|^{\aleph_0},$ where $|\mathbb{F}|$ is the cardinality of the field $\mathbb{F}.$
