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On quantum shuffle and quantum affine algebras

Pascal Grosse
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Abstract

A construction of the quantum affine algebra $U_q(g)$ is given in two steps. We explain how to obtain the algebra from its positive Borel subalgebra $U_q(b^+)$, using a construction similar to Drinfeld's quantum double. Then we show how the positive Borel subalgebra can be constructed with quantum shuffles.

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Pascal Grosse. 2001-07-24. On quantum shuffle and quantum affine algebras. https://arxiv.org/abs/math/0107176

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