Gröbner–Shirshov Bases for Lie Superalgebras and Their Universal Enveloping Algebras

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.