Symbolic computation in cubic Jordan matrix algebras and in related structures

TL;DR

This paper introduces CubicJordanMatrixAlg, a GAP package for symbolic algebra computations in cubic Jordan matrix algebras and related structures, enabling new calculations in Lie theory.

Contribution

The paper presents a new GAP package for symbolic computations in cubic Jordan matrix algebras and demonstrates its application to Lie-theoretic group relations.

Findings

Successfully computed commutator relations in F4-graded groups.

Enabled new algebraic calculations in cubic Jordan matrix algebras.

Provided a tool for further research in related algebraic structures.

Abstract

We present CubicJordanMatrixAlg, a GAP package for symbolic computation in cubic Jordan matrix algebras and in related Lie-theoretic structures. As an application, we use it to compute certain (commutator) relations in $F_4$-graded groups that were constructed by De Medts and the author from cubic Jordan matrix algebras.