On the universal sl₂ invariant of Brunnian bottom tangles

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A link L is called Brunnian if every proper sublink of L is trivial. Similarly, a bottom tangle T is called Brunnian if every proper subtangle of T is trivial. In this paper, we give a small subalgebra of the n-fold completed tensor power of Uₕ(sl₂) in which the universal sl₂ invariant of n-component Brunnian bottom tangles takes values. As an application, we give a divisibility property of the colored Jones polynomial of Brunnian links.