Formally-radical Functions in Elements of a Nilpotent Lie Algebra and Noncommutative Localizations.

In the present paper, we introduce the sheaf 픗픤 of germs of non-commutative holomorphic functions in elements of a finite-dimensional nilpotent Lie algebra 픤, which is a sheaf of non-commutative Fréchet algebras over the character space of 픤. We prove that 픗픤(D) is a localization over the universal enveloping algebra ${\mathcal U}({\mathfrak g})$ whenever D is a polydisk, which in turn allows to describe the Taylor spectrum of a supernilpotent Lie algebra of operators in terms of the transversality. [ABSTRACT FROM AUTHOR]