Local left invertibility for operator tuples and noncommutative localizations


Dosiev A.

JOURNAL OF K-THEORY, vol.4, no.1, pp.163-191, 2009 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 4 Issue: 1
  • Publication Date: 2009
  • Doi Number: 10.1017/is008008021jkt064
  • Journal Name: JOURNAL OF K-THEORY
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.163-191
  • Keywords: Arens-Michael envelope, noncommutative localization, entire functions in elements of a nilpotent Lie algebra, homological dimensions, NILPOTENT LIE-ALGEBRA, COHOMOLOGY, ELEMENTS, SPECTRA

Abstract

In the paper we propose an operator approach to the noncommutative Taylor localization problem based on the local left invertibility for operator tuples acting on a Frechet space. We prove that the canonical homomorphism U(g) -> O(g) of the universal enveloping algebra U(g) of a nilpotent Lie algebra g into its Arens-Michael envelope O(g) is the Taylor localization whenever g has normal growth.