Abstract

We explain a Macaulay2 implementation of a construction of Holweck and Oeding (J. Comput. Sci. 82 (2024), art. id. 102431) of a graded algebra structure on the direct sum of a Lie algebra $\mathfrak{𝔤}$ (typically ${\mathfrak{𝔰}\mathfrak{𝔩}}_n$) and a $\mathfrak{𝔤}$-module (typically a subspace of an exterior algebra ${\wedge <!--FUNCTION\; APPLICATION-->}^{\bullet }{ℂ}^n$). We implement brackets, a Killing form, matrix representations of adjoint operators, and ranks of blocks of their powers.

Keywords

Mathematical Subject Classification

Supplementary material

ExteriorExtensions.m2

Milestones

Authors