English

The basic bundle gerbe on unitary groups

Differential Geometry 2009-11-13 v1 Mathematical Physics math.MP

Abstract

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.

Keywords

Cite

@article{arxiv.0804.3464,
  title  = {The basic bundle gerbe on unitary groups},
  author = {Michael K Murray and Danny Stevenson},
  journal= {arXiv preprint arXiv:0804.3464},
  year   = {2009}
}
R2 v1 2026-06-21T10:33:24.908Z