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

DOSİ A.

Algebra Colloquium, cilt.17, sa.SPEC. ISSUE 1, ss.749-788, 2010 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 17 Sayı: SPEC. ISSUE 1
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1142/s1005386710000726
  • Dergi Adı: Algebra Colloquium
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.749-788
  • Anahtar Kelimeler: formally-radical functions, non-commutative holomorphic functions in elements of a Lie algebra, non-commutative localization, Taylor spectrum, transversality
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.