Homological Dimensions of the Algebra Formed by Entire Functions of Elements of a Nilpotent Lie Algebra

A. A. Dosiev

Funkcionalʹnyj analiz i ego priloženiâ, Tome 37 (2003) no. 1, pp. 73-77

Résumé

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 $\mathcal{U}(\mathfrak{g})\to\mathcal{O}_{\mathfrak{g}}$ of the universal enveloping algebra $\mathcal{U}(\mathfrak{g})$ of $\mathfrak{g}$ into its Arens–Michael hull $\mathcal{O}_{\mathfrak{g}}$ is an absolute localization in the sense of Taylor provided that $[\mathfrak{g},[\mathfrak{g},\mathfrak{g}]]=0$.

Détail

Keywords: Arens–Michael hull, projective homological dimension, nilpotent Lie algebra, localization, Taylor spectrum.