Transgressive loop group extensions

Abstract

A central extension of the loop group of a Lie group is called transgressive, if it corresponds under transgression to a degree four class in the cohomology of the classifying space of the Lie group. Transgressive loop group extensions are those that can be explored by finite-dimensional, higher-categorical geometry over the Lie group. We show how transgressive central extensions can be characterized in a loop-group theoretical way, in terms of loop fusion and thin homotopy equivariance.

37 pages, 3 figures. In v2 the former Section 3.3 about Lie algebra splittings was withdrawn because of a gap in the proof of former Theorem 3.3.3. Best possible statement about Lie algebra splittings is now Proposition 4.9. In v3 typos and a mistake in Example 2.6 have been corrected; v3 is the published version

References in corpus (2)

• More Morphisms between Bundle Gerbes
• Polyakov-Wiegmann Formula and Multiplicative Gerbes

Cited by in corpus (4)

• Higher Gauge Theory and Integrability
• The classification of chiral WZW models by $H_{+}^4(BG,\mathbb{Z})$
• Connes fusion of spinors on loop space
• Loop groups and noncommutative geometry