Formally-radical functions in elements of a nilpotent Lie algebra and noncommutative localizations
Algebra Colloquium, cilt.17, sa.SPEC. ISSUE 1, ss.749-788, 2010 (SCI-Expanded, Scopus)
- 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.