ExteriorExtensions: A package for Macaulay2

Abstract

We explain a Macaulay2 implementation of a construction, which appeared in [Holweck-Oeding arXiv:2206.13662], of a graded algebra structure on the direct sum of a Lie algebra $\mathfrak{g}$ (typically $\mathfrak{sl}_n$) and a $\mathfrak{g}$-module (typically a subspace of an exterior algebra $\bigwedge^{\bullet}\mathbb{C}^n$). We implement brackets, a Killing form, matrix representations of adjoint operators and ranks of blocks of their powers.