Classification of simple q_2-supermodules

TL;DR

This paper classifies all simple supermodules over the queer Lie superalgebra _{2}, providing a comprehensive understanding of their structure through algebraic classification methods.

Contribution

It introduces a complete classification of simple supermodules over _{2} using Euclidean ring equivalence classes, a novel approach in this context.

Findings

Complete classification of simple supermodules over _{2}

Connection between supermodules and Euclidean ring elements

Advancement in understanding queer Lie superalgebra representations

Abstract

We classify all simple supermodules over the queer Lie superalgebra $\mathfrak{q}_{2}$ up to classification of equivalence classes of irreducible elements in a certain Euclidean ring.