We show that a set of monic polynomials in a free Lie superalgebra is a Grobner᎐Shirshov basis for a Lie superalgebra if and only if it is ä Grobner᎐Shirshov basis for its universal enveloping algebra. We investigate thë structure of Grobner᎐Shirshov bases for Kac᎐Moody superalgebras and givë explicit constructions of Grobner᎐Shirshov bases for classical Lie superalgebras.
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