Grobner-Shirshov bases for classical Lie superalgebras and their enveloping algebras

Abstract

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