Abstract
We show that a set of monic polynomials in a free Lie superalgebra is a Gröbner–Shirshov basis for a Lie superalgebra if and only if it is a Gröbner–Shirshov basis for its universal enveloping algebra. We investigate the structure of Gröbner–Shirshov bases for Kac–Moody superalgebras and give explicit constructions of Gröbner–Shirshov bases for classical Lie superalgebras.
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