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WHEN IS A COMPLETION OF THE UNIVERSAL ENVELOPING ALGEBRA A BANACH PI-ALGEBRA?
Published online by Cambridge University Press: 05 September 2022
Abstract
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
$\mathfrak {n}$
.
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- Research Article
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- © The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.
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