论文标题
当通用包裹的代数完成时，是Banach Pi-Algebra吗？
When a completion of the universal enveloping algebra is a Banach PI-algebra?
论文作者
论文摘要
我们证明，一个有限维综合体的普遍包围代数的Banach代数$ b $ lie代数为代数$ \ mathfrak {g} $，并且仅当nilpotent the nilpotent the nilpotent $ \ mathfrak {n} $ of Mathfrak of $ \ mathfrak $ b $ niltife and nilpotent and of nilpotent of nilpotent of nilpotent n nilpot。此外，仅当$ \ mathfrak {n} $满足某个多项式增长条件时，这才能保持。
We prove that a Banach algebra $B$ that is a completion of the universal enveloping algebra of a finite-dimensional complex Lie algebra $\mathfrak{g}$ satisfies a polynomial identity if and only if the nilpotent radical $\mathfrak{n}$ of $\mathfrak{g}$ is associatively nilpotent in $B$. Furthermore, this holds if and only if a certain polynomial growth condition is satisfied on $\mathfrak{n}$.
