The moduli space of $1|1$-dimensional complex associative algebras

TL;DR

This paper thoroughly analyzes the moduli space of 1|1-dimensional complex associative algebras, providing detailed cohomology calculations and deformation classifications for all elements.

Contribution

It offers a complete classification of the moduli space, including cohomology and versal deformations, which was previously unexplored for this algebraic structure.

Findings

Complete cohomology calculations for all elements.

Classification of versal deformations.

Detailed structure of the moduli space.

Abstract

In this paper, we study the moduli space of $1|1$-dimensional complex associative algebras. We give a complete calculation of the cohomology of every element in the moduli space, as well as compute their versal deformations.