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

Abstract

We show that a set of monic polynomials in the 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.