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The Drinfeld associator of gl(1|1)

Jens Lieberum
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Abstract

We determine explicitly a rational even Drinfeld associator Q in a completion of the universal enveloping algebra of the Lie superalgebra gl(1|1)^3. More generally, we define a new algebra of trivalent diagrams that has a unique even horizontal group-like Drinfeld associator P. The associator P is mapped to Q by a weight system. As a result of independent interest, we show how O. Viro's generalization Delta^1 of the multi-variable Alexander polynomial can be obtained from the universal Vassiliev invariant of trivalent graphs. We determine P by using the invariant Delta^1(T) of a planar tetrahedron T.

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Jens Lieberum. 2002-04-30. The Drinfeld associator of gl(1|1). https://arxiv.org/abs/math/0204346

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