Super-representations of quivers and related polynomial semi-invariants

TL;DR

This paper introduces super-representations of quivers and characterizes their polynomial semi-invariants and invariants over fields of characteristic zero, expanding the algebraic understanding of quiver representations.

Contribution

It defines super-representations of quivers and describes the associated polynomial semi-invariants and invariants, a novel extension in the theory of quiver representations.

Findings

Characterization of polynomial semi-invariants for super-representations

Description of polynomial invariants in the super-representation context

Extension of classical invariant theory to super-representations

Abstract

We introduce the notion of a super-representation of a quiver. For super-representations of quivers over a field of characteristic zero, we describe the corresponding (super)algebras of polynomial semi-invariants and polynomial invariants.