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GradedLieAlgebras -- a package for doing computations in graded Lie algebras


This package provides routines for doing computations in graded Lie algebras.

The package relies on algorithmic theory on graded Lie algebras developed by Clas Löfwall and Jan-Erik Roos in A Nonnilpotent 1-2-Presented Graded Hopf Algebra Whose Hilbert Series Converges in the Unit Circle, Adv. Math. 130 (1997), no. 2, 161–200.


for some illustrations of ways to use this package.


Computations with squares in characteristic 2 is not supported in the current version.


Certification a gold star

Version 3.0 of this package was accepted for publication in volume 11 of The Journal of Software for Algebra and Geometry on 28 August 2020, in the article Software for doing computations in graded Lie algebras (DOI: 10.2140/jsag.2021.11.9). That version can be obtained from the journal or from the Macaulay2 source code repository.


This documentation describes version 3.0 of GradedLieAlgebras.

Source code

The source code from which this documentation is derived is in the file GradedLieAlgebras.m2. The auxiliary files accompanying it are in the directory GradedLieAlgebras/.


For the programmer

The object GradedLieAlgebras is a package.