On the Canonical Construction of Simple Lie Superalgebras

TL;DR

This paper introduces a unified method for constructing simple Lie superalgebras from root systems, focusing on bases with minimal isotropic roots, advancing the structural understanding of these algebraic objects.

Contribution

It provides a canonical construction approach for simple Lie superalgebras based on abstract root systems with minimal isotropic roots, enhancing previous classification methods.

Findings

Unified construction method for simple Lie superalgebras

Identification of bases with minimal isotropic roots

Clarification of the relationship between root systems and superalgebras

Abstract

Axioms for the generalization of root systems were defined and classified (irreducible) by V. Serganova, which precisely correspond to the root systems of basic classical Lie Superalgebras. Here, we present a unified method for constructing simple Lie Superalgebras from the abstract root system, with the choice of base having the minimal number of isotropic roots.