The moduli of representations of degree 2

TL;DR

This paper constructs moduli spaces for various types of 2-dimensional representations across groups, monoids, and associative algebras, categorizing them by properties like irreducibility and mold types.

Contribution

It introduces a comprehensive framework for constructing moduli of 2-dimensional representations for different algebraic structures and mold types.

Findings

Constructed moduli spaces for six types of 2D representations.

Unified approach applicable to groups, monoids, and associative algebras.

Framework covers irreducible, Borel, semi-simple, unipotent, and scalar molds.

Abstract

There are 6 types of 2-dimensional representations in general. For any groups and any monoids, we can construct the moduli of 2-dimensional representations for each type: the moduli of absolutely irreducible representations, representations with Borel mold, representations with semi-simple mold, representations with unipotent mold, representations with unipotent mold over ${\Bbb F}_2$, and representations with scalar mold. We can also construct them for any associative algebras.