Representations of the super Jordan plane

TL;DR

This paper classifies simple and indecomposable finite-dimensional representations of the super Jordan plane, revealing their structure and providing explicit families of higher-dimensional indecomposables.

Contribution

It introduces a complete classification of simple and low-dimensional indecomposable representations of the super Jordan plane, and constructs new families of higher-dimensional indecomposables.

Findings

Simple representations are one-dimensional.

Classified indecomposables of dimension 2 and 3.

Presented two families of indecomposables of arbitrary dimension.

Abstract

It is shown that the finite-dimensional simple representations of the super Jordan plane $B$ are one-dimensional. The indecomposable representations of dimension $2$ and $3$ of $B$ are classified. Two families of indecomposable representations of $B$ of arbitrary dimension are presented.