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arXiv · 1810.13213

Arens-Michael envelopes of nilpotent Lie algebras, holomorphic functions of exponential type, and homological epimorphisms

Oleg Aristov
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Abstract

Our aim is to give an explicit description of the Arens-Michael envelope for the universal enveloping algebra of a finite-dimensional nilpotent complex Lie algebra. It turns out that the Arens-Michael envelope belongs to a class of completions introduced by R.~Goodman in 70s. To find a precise form of this algebra we preliminary characterize the set of holomorphic functions of exponential type on a simply connected nilpotent complex Lie group. This approach leads to unexpected connections to Riemannian geometry and the theory of order and type for entire functions. As a corollary, it is shown that the Arens-Michael envelope considered above is a homological epimorphism. So we get a positive answer to a question investigated earlier by Dosi and Pirkovskii.

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Oleg Aristov. 2018-10-31. Arens-Michael envelopes of nilpotent Lie algebras, holomorphic functions of exponential type, and homological epimorphisms. https://doi.org/10.1090/mosc%2F301

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