Infinitesimal Symmetries of Dixmier-Douady Gerbes

Abstract

We introduce the infinitesimal symmetries of Dixmier-Douady gerbes over a manifold M, both with and without connective structures and curvings. We explore the algebraic structure possessed by these symmetries, and relate them to equivariant gerbes via a "differentiation functor". In the case that a gerbe G is equipped with a connective structure A, we give a new construction of the Courant algebroid associated to (G,A) directly in terms of the infinitesimal symmetries of (G,A).

References in corpus (2)

• Introduction to the language of stacks and gerbes
• Courant algebroids from categorified symplectic geometry

Cited by in corpus (7)

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• Nonabelian higher derived brackets
• Multiplicative vector fields on bundle gerbes
• Towards an extended/higher correspondence -- Generalised geometry, bundle gerbes and global Double Field Theory
• Deformations of generalized complex branes
• Gerbes in Geometry, Field Theory, and Quantisation