可换环上一类矩阵李代数的导子及自同构

Derivations and Automorphisms of a Matrix Lie Algebra Over a Commutative Ring

以一类非可解矩阵李代数L为研究对象,利用分块矩阵的乘法运算,对L的导子及自同构进行了研究.借助于一种构造性证明的方法,证明了L的中心平凡且导子均为内导子,即L是完备李代数,并在R是特征不为2的整环的条件下,决定了L的所有自同构.

Based on a non-solvable matrix Lie algebra L , the derivations and automorphisms of L were studied by the multiplication operation of block matrix. Using constructive proof methods, it is proved that the center of L is trivial and all its derivations are inner, in other words, L is shown to be a complete Lie algebra. Then, when R is an integer ring and its character is not 2, all the automorphisms of L are determined.