Abstract
AbstractWe prove that a Banach algebraBthat 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 inB. Furthermore, this holds if and only if a certain polynomial growth condition is satisfied on$\mathfrak {n}$.
Publisher
Cambridge University Press (CUP)
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