Gröbner-Shirshov bases for lie superalgebras and their universal enveloping algebras

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. © 1999 Academic Press.