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

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

1998-09-06

arxiv.org/abs/math/9809024v1

Mathematics

Representation Theory

36 pages

Scientific paper

We show that a set of monic polynomials in the 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.

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