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arXiv · 0804.3464

The basic bundle gerbe on unitary groups

Michael K Murray·Danny Stevenson
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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.

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Michael K Murray, Danny Stevenson. 2008-04-22. The basic bundle gerbe on unitary groups. https://doi.org/10.1016/j.geomphys.2008.07.006

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