2008/04/22 by Michael K. Murray, Michael K Murray, Danny Stevenson · 18 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebra over a field #Bundle #Computer science #Connection (principal bundle) #Geometry #Group (periodic table) #Hilbert space #Holomorphic function #Ideal (ethics) #Identity (music) #Law #Mathematics #Physics #Pure mathematics #Space (punctuation) #Unitary state #math-ph #math.DG #math.MP #msc:47A60 #msc:55R65
paper · pdf · doi:10.1016/j.geomphys.2008.07.006
published in Journal of Geometry and Physics 58(11), 1571-1590 (Elsevier BV)
arxiv created 2008/04/22 · openalex publication_date 2008/07/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the construction of the basic bundle gerbe on SU(n) introduced by Meinrenken and show that it extends to a range of groups with unitary actions on a Hilbert space including U(n), diagonal tori and the Banach Lie group of unitary operators differing from the identity by an element of a Schatten ideal. In all these cases we give an explicit connection and curving on the basic bundle gerbe and calculate the real Dixmier-Douady class. Extensive use is made of the holomorphic functional calculus for operators on a Hilbert space.