In the notebook and the packages we define basic operations for Lie algebras of matrices, and calculate the Killing forms of the following Lie algebras: the general linear ...

This package supports computation in a graded free Lie algebra. It generates a basis of the space of all products (up to a given maximum degree) as well as all commutators. A ...

We give the classification of the graded algebras for a class of nilpoint Lie algebra which extends the graded filiform Lie algebras Vergne's classification [3]. That general ...

We present the Mathematica application ‘‘LieART’’ (Lie Algebras and Representation Theory) for computations frequently encountered in Lie algebras and representation ...

Numerical procedures for obtaining the root systems of both classical and exceptional Lie algebras are slow and tedious when done by hand. This is a contribution in the field ...

The purpose of this program is to derive the determining equations for Lie-point symmetries. The determining equations are derived in a form simplified as far as possible. ...

In this paper we describe some Leibniz algebras whose corresponding Lie algebra is four-dimensional Diamond Lie algebra D and the ideal generated by the squares of elements ...

We show how the features of Mathematica can be used in the classification of the filiform Lie algebras. We reduce the parameters which define a family of filiform Lie ...

This notebook has a dual purpose. As first, it roughly implements the octonionic multiplication and calculates the commutator relations of the Lie algebra g2. As second, it ...

This package constructs an orthonormal Basis of su(n). Additionally there are functions that compute the adjoint representation (structure constants) and the Killing form for ...