The basic bundle gerbe on unitary groups

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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• WZW branes and gerbes
• Index Theory, Gerbes, and Hamiltonian Quantization
• Basic gerbe over non simply connected compact groups
• Higher-Degree Analogs of the Determinant Line Bundle
• Higher bundle gerbes and cohomology classes in gauge theories
• Gerbes on complex reductive Lie groups
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Cited by in corpus (11)

• Differential topology of semimetals
• Square root of gerbe holonomy and invariants of time-reversal-symmetric topological insulators
• Categorical Structures on Bundle Gerbes and Higher Geometric Prequantisation
• Basic equivariant gerbes on non-simply connected compact simple Lie groups
• The Weyl map and bundle gerbes
• Extensions of Lattice Groups, Gerbes and Chiral Fermions on a Torus
• Exponential Functors, R-Matrices and Twists
• Equivariant higher twisted K-theory of SU(n) for exponential functor twists
• Bundle gerbes and the Weyl map
• Topological Insulators and the Kane-Mele Invariant: Obstruction and Localisation Theory
• Spectral Sequence Computation of Higher Twisted $K$-Groups of $SU(n)$