Gerbes and Lie Groups

Details Gerbes and Lie Groups Gerbes and Lie Groups

2007-10-29

arxiv.org/abs/0710.5467v1

Mathematics

Differential Geometry

29 pages, appears in "Trends and Developments in Lie Theory", Progress in Math., Birkhaeuser

Scientific paper

We present a review of bundle gerbes, emphasizing their relations to Lie groups. Indeed, compact Lie groups do not only carry the structure of a Riemannian manifold, but also canonical families of bundle gerbes. We recall the construction of these bundle gerbes and their relation to loop groups. We discuss several algebraic structures for bundle gerbes with connection such as Jandl structures, gerbe modules and gerbe bimodules, and indicate their applications to Wess-Zumino terms in two-dimensional field theories.

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