完备Witt李代数的导子与自同构群
Derivations and automorphism groups of completed Witt Lie algebra
摘要：
本文引入了一个简单的李代数，称为完备Witt李代数.完整地描述了它的导子代数和自同构群。作为副产品，得到了这个李代数的第一上同调群是平凡的，其系数在其伴随模中。进一步，我们完全确定了该李代数在其自同构群下的共轭类，并且得到了该李代数不含任何非零ad-局部有限元.
英文摘要：
In this paper, a simple Lie algebra, referred to as the completed Witt Lie algebra, is introduced. Its derivation algebra and automorphism group are completely described. As a byproduct, it is obtained that the first cohomology group of this Lie algebra with coefficients in its adjoint module is trivial. Furthermore, we completely determine the conjugate classes of this Lie algebra under its automorphism group, and also obtain that this Lie algebra does not contain any nonzero ad-locally finite element.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
