The basic gerbe over a compact simple Lie group

Abstract

Let $G$ be a compact, simply connected simple Lie group. We give a construction of an equivariant gerbe with connection on $G$, with equivariant 3-curvature representing a generator of $H_G^3(G,\mathbb{Z})$. Technical tools developed in this context include a gluing construction for gerbes and a theory of equivariant bundle gerbes.

19 pages. To appear in L'Enseignement Mathematique

References in corpus (3)

• WZW branes and gerbes
• Chern character in twisted K-theory: equivariant and holomorphic cases
• Connections and curvings on lifting bundle gerbes

Cited by in corpus (15)

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• Chern character in twisted K-theory: equivariant and holomorphic cases
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• Fusion of symmetric $D$-branes and Verlinde rings
• String geometry vs. spin geometry on loop spaces
• Transgressive loop group extensions
• Twisted conjugacy classes, coadjoint orbits of loop groups and D-branes in the WZW-model
• Exponential Functors, R-Matrices and Twists
• Multiplicative Bundle Gerbes with Connection
• Gerbes in Geometry, Field Theory, and Quantisation
• K-twisted K-theory for SU(N)
• Equivariant gerbes over compact simple Lie groups
• Momentum Maps and Morita Equivalence