Abstract
This note deals with homological characteristics of algebras of holomorphic functions of noncommuting variables generated by a finite-dimensional nilpotent Lie algebra \(\mathfrak{g}\). It is proved that the embedding \(U(\mathfrak{g}) \to O_\mathfrak{g} \) of the universal enveloping algebra \(U\left( \mathfrak{g} \right)\) of \(\mathfrak{g}\) into its Arens–Michael hull \(O_\mathfrak{g} \) is an absolute localization in the sense of Taylor provided that \(\left[ {\mathfrak{g},\left[ {\mathfrak{g},\mathfrak{g}} \right]} \right] = {\text{0}}\)
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Dosiev, A.A. Homological Dimensions of the Algebra Formed by Entire Functions of Elements of a Nilpotent Lie Algebra. Functional Analysis and Its Applications 37, 61–64 (2003). https://doi.org/10.1023/A:1022976011347
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DOI: https://doi.org/10.1023/A:1022976011347