The basic bundle gerbe on unitary groups

JOURNAL OF GEOMETRY AND PHYSICS

卷:58

Article

Murray, Michael²  Stevenson, Danny¹ 

[1] Univ Hamburg, Fachbereich Math, D-20146 Hamburg, Germany

[2] Univ Adelaide, Sch Math Sci, Adelaide, SA 5005, Australia

关键词: Bundle gerbes;    Unitary groups;    Holomorphic functional calculus;    Connection;   

DOI  :  10.1016/j.geomphys.2008.07.006

来源: Elsevier

【 摘 要 】

We consider the construction of the basic build le 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) and Up(H), the Banach Lie group Of unitaries differing from the identity by ail element of a Schatten ideal. In all these cases we give ail 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. (C) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

Free