Relationship of the Hennings and Witten–Reshetikhan–Turaev invariants for higher rank quantum groups

Abstract

The Hennings invariant for the small quantum group associated to an arbitrary simple Lie algebra at a root of unity is shown to agree with the Witten–Reshetikhin–Turaev (WRT) three-manifold invariant arising from Chern–Simons field theory for the same Lie algebra and the same root of unity on all integer homology three-spheres, at roots of unity where both are defined. This partially generalizes the work of Chen et al. [On the relation between the WRT invariant and the Hennings invariant, Math. Proc. Cambridge Philos. Soc. 146(1) (2009) 151–163; Three-manifold invariants associated with restricted quantum groups, Math. Z. 272(3–4) (2012) 987–999] which relates the Hennings and WRT invariants for [Formula: see text] and [Formula: see text] for arbitrary rational homology three-spheres.