Abstract
M. Hennings and G. Kuperberg defined quantum invariants Z_{\rm Henn} and Z_{\rm Kup} of closed oriented 3-manifolds based on certain Hopf algebras, respectively. We prove that |Z_{\rm Kup}|=|Z_{\rm Henn}|^2 for lens spaces when both invariants are based on factorizable finite dimensional ribbon Hopf algebras.
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