Jordan Algebras of Symmetric Matrices

This page contains supplementary code to the following paper:

Arthur Bik, Henrik Eisenmann, and Bernd Sturmfels: Jordan algebras of symmetric matrices

In: Le Matematiche, 76 (2021) 2, p. 337-353

DOI: 10.4418/2021.76.2.3 ARXIV: https://arxiv.org/abs/2010.00277 CODE: https://mathrepo.mis.mpg.de/JordanAlgebrasSymmetricMatrices

In Theorem 2.7, we classify the unital Jordan algebras of dimension 3. We used SAGE to translate the Jordan axiom into conditions on the structure constants defining the Jordan algebra in certain cases.

• Equations defining a Jordan algebra

In Example 6.10, we find the quadrics in dual Pluecker coordinates that vanish on the congruence orbits of the nets \(\mathcal{L}_1\), \(\mathcal{L}_2\) and \(\mathcal{L}_3\) from Example 6.9.

• Quadrics vanishing on orbits in Pluecker coordinates

The output files of the computations can be downloaded here:

L1res.txt

L2res.txt

L3res.txt

Project page created: 27/10/2020

Code contributors: Arthur Bik

Code written by: Arthur Bik, 27/10/2020

Corresponding author of this page: Arthur Bik, arthur.bik@mis.mpg.de

Project contributors: Arthur Bik

Software used: SageMath