Defining Relations for Lie Superalgebras with Cartan matrix

TL;DR

This paper provides a comprehensive description of the presentations of certain simple Z-graded Lie superalgebras with Cartan matrices, including non-Serre relations and cases with infinitely many relations.

Contribution

It offers the first complete classification of presentations for these Lie superalgebras, including non-integer and non-symmetrizable matrices, expanding understanding beyond classical cases.

Findings

Descriptions of presentations including non-Serre relations

Identification of cases with infinitely many relations

Applicability to related Lie algebras

Abstract

We completely describe presentations of Lie superalgebras with Cartan matrix if they are simple Z-graded of polynomial growth. Such matrices can be neither integer nor symmetrizable. There are non-Serre relations encountered. In certain cases there are infinitely many relations. Our results are applicable to the Lie algebras with the same Cartan matrices as the Lie superalgebras considered.