SymboLie

A Mathematica program
for determining optimal systems of families of Lie subalgebras

SymboLie is a package written in the Wolfram Language designed to automatically determine optimal systems of families of Lie subalgebras of a finite-dimensional Lie algebra.

Papers related to SymboLie:

• L. Amata, F. Oliveri. Automatic determination of optimal systems of Lie subalgebras: the package SymboLie. Contemporary Mathematics, 789, 1-17, 2023. Paper
• L. Amata, F. Oliveri, E. Sgroi. Optimal Systems of Families of Lie Subalgebras: A Computational Approach. Submitted, 2024.
• L. Amata, F. Oliveri, E. Sgroi. Symbolic computation of optimal systems of subalgebras of three and four--dimensional real Lie algebras. Submitted, 2024.

Mathematica Source Code of SymboLie

Below you may download some Mathematica Notebooks where SymboLie is used.

• Algebra of traceless 2x2 matrices: Mathematica Notebook; PDF.
• Algebra of Lie symmetries of KdV equation: Mathematica Notebook; PDF.
• Algebra of Lie symmetries of Burgers' equation: Mathematica Notebook; PDF.
• Algebra of Lie symmetries of 2D stable viscous gas equations: Mathematica Notebook; PDF.
• Algebra of Lie symmetries of linear Heat equation: Mathematica Notebook; PDF.
• 6D Algebra (Ovsiannikov): Mathematica Notebook; PDF.
• 3D Real Lie Algebras: Mathematica Notebook; PDF.
• 4D Real Lie Algebras: Mathematica Notebook; PDF.