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

Leonid A. Bokut·Seok-Jin Kang·Kyu-Hwan Lee·Peter Malcolmson
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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.

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Leonid A. Bokut, Seok-Jin Kang, Kyu-Hwan Lee, Peter Malcolmson. 1998-09-06. Gröbner-Shirshov Bases for Lie Superalgebras and Their Universal Enveloping Algebras. https://arxiv.org/abs/math/9809024

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