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The van Est homomorphism for strict Lie 2-groups

Published 16 May 2024 in math.DG, math-ph, math.MP, and math.SG | (2405.09969v1)

Abstract: We construct a van Est map for strict Lie 2-groups from the Bott-Shulman-Stasheff double complex of the strict Lie 2-group to the Weil algebra of its associated strict Lie 2-algebra. We show that, under appropriate connectedness assumptions, this map induces isomorphisms in cohomology. As an application, we differentiate the Segal 2-form on the loop group.

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