Gröbner–Shirshov bases for some Lie algebras

Resumo

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