Non-commutative holomorphic functions in elements of a Lie algebra and the absolute basis problem

Dosi (Dosiev) A. A.

IZVESTIYA MATHEMATICS, vol.73, no.6, pp.1149-1171, 2009 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 73 Issue: 6
  • Publication Date: 2009
  • Doi Number: 10.1070/im2009v073n06abeh002476
  • Journal Name: IZVESTIYA MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1149-1171
  • Middle East Technical University Affiliated: No

Abstract

We study the absolute basis problem in algebras of holomorphic functions in non-commuting variables generating a finite-dimensional nilpotent Lie algebra g. This is motivated by J. L. Taylor's programme of non-commutative holomorphic functional calculus in the Lie algebra framework.