论文标题
在交换涉及环上的lie矩阵环上的局部和2个本地派生
Local and 2-local derivations on Lie matrix rings over commutative involutive rings
论文作者
论文摘要
在本文中，我们证明，在交换性$*$ - 环上的偏度矩阵的谎言环上的每个2个本地内部派生是一个内部派生。我们还将技术应用于一个集合的无限维偏度矩阵值图的各种代数，并证明此类代数上的每个2个空间空间衍生物都是空间衍生。我们还表明，上述代数上的每个局部空间派生都是派生。
In the present paper we prove that every 2-local inner derivation on the Lie ring of skew-adjoint matrices over a commutative $*$-ring is an inner derivation. We also apply our technique to various Lie algebras of infinite-dimensional skew-adjoint matrix-valued maps on a set and prove that every 2-local spatial derivation on such algebras is a spatial derivation. We also show that every local spatial derivation on the above Lie algebras is a derivation.
