Formally-radical functions in elements of a nilpotent Lie algebra and noncommutative localizations

DOSİ A.

Algebra Colloquium, vol.17, no.SPEC. ISSUE 1, pp.749-788, 2010 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 17 Issue: SPEC. ISSUE 1
  • Publication Date: 2010
  • Doi Number: 10.1142/s1005386710000726
  • Journal Name: Algebra Colloquium
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.749-788
  • Keywords: formally-radical functions, non-commutative holomorphic functions in elements of a Lie algebra, non-commutative localization, Taylor spectrum, transversality
  • Middle East Technical University Affiliated: Yes

Abstract

In the present paper, we introduce the sheaf g of germs of non-commutative holomorphic functions in elements of a finite-dimensional nilpotent Lie algebra g, which is a sheaf of non-commutative Fréchet algebras over the character space of . We prove that ℐg(D) is a localization over the universal enveloping algebra U(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. © 2010 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and Suzhou University.