A package for Macaulay2 that constructs extensions of Lie algebras via exterior algebras
This package builds a graded algebra that equivariantly extends the Lie algebra sl_n via the non-zero graded piece of the exterior algebra by defining the bracket products. Constructs matrix representations of adjoint operators. Computes ranks of blocks coming from the grading.
Keywords "Lie Algebras", "Jordan Decomposition", "Tensor invariants"
To interact with the package save the file somewhere on your machine. Then launch Macaulay M2 from the same directory. Then do this:
installPackage("ExteriorExtensions")
viewHelp ExteriorExtensions
The help documents give several basic examples to try out.
Subsequent times when you start M2, do this (this doesn’t re-generate the examples).
loadPackage ExteriorExtensions
Details on the package can be found on the arXiv. This article was accepted for publication at JSAG July 2025.