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We give Gröbner–Shirshov bases for the Drinfeld–Kohno Lie algebra Ln in [1] and the Kukin Lie algebra AP in [2], where P is a semigroup. By way of application, we show that Ln is free as a ℤ-module and exhibit a ℤ-basis for Ln. We give another proof of the Kukin Theorem: If P has the undecidable word problem then so isAP.
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